The title itself is part of the geek charm of this British comedy centered around three guys and a pub where time leaks create a fascinating night for them.  It is laced with gag references to science fiction and fantasy tropes and the world of geek chic.  As a time travel story it ultimately fails, but has a lot of fun doing so, and is well worth watching.

Ray, Toby, and Pete leave a bad movie to drop into a pub for a pint, or several pints.  Ray favors everything geek except the labels; he insists that they should not call themselves "nerds" but "imagineers".  Toby (sometimes called "Tobe") is more a geek wannabe, nowhere near as informed or eager as Ray, but has aspirations to be a filmwriter.  Pete is the kind of geek who thinks that if he at least pretends he knows nothing about geek culture he's not a geek.  Having just watched a bad movie, the trio decide to write a letter to Hollywood to tell them how to make better movies, and Toby tears a page out of his script ideas notebook on which to write it.

The event rundown from there, in the order we see it, starts with Ray meeting a girl named Cassie in the cozy, a smaller adjacent room; Cassie says that she is a time traveler who works fixing time leaks, but she wanted to take the opportunity to meet him because he will be famous.  He believes his friends hired her as a gag, and tells them the story; they believe he has invented it.

Clean-shaven Pete leaves for the bathroom, saying that when he returns they should leave for a different pub; when he returns, however, everyone in the room is dead, including a version of himself with a heavy growth of beard.  He runs back to the gents', then decides to slip away; but when he is doing this, he hears talk in the pub and follows it back.  The song he was singing when he left is finishing on the juke box, and his friends are fine, and now they don't believe his story.  He persuades them to enter the gents', and when they emerge they are in the past, less than an hour.  Ray hides them in a closet.

He remembers that Cassie is talking to him in the cozy, and intercepts her leaving; now she thinks he is mocking her when he tells her the leak is in the men's room, storms out, and returns the next instant, six months later for her.  She assures him that she has fixed everything, but they should simply wait for their selves to enter the gents' and then return to the bar.  They are doing this, stop to use the bathroom, and knowing that their other selves just entered the gents' they use the ladies', where another time leak sends them to a post-apocalyptic future.  Pete immediately re-enters the ladies', but before Ray and Toby can decide whether to follow he emerges from the gents with the full beard he previously saw, raving about the dangers.

They scrounge warmer clothes and weapons, and discover a mural of themselves dressed in the clothes they just donned sitting at their table in the bar holding that letter.  They then re-enter the gents, encounter themselves, and emerge in a near-future at a fan party for them.  Another time traveler, Millie, meets them there and returns them (by way of the gents') to their own time.  Cassie arrives and discovers Millie's involvement; but Millie's intention is to kill the trio immediately after they have written that famous paper.  In a major confrontation, she kills everyone and leaves.  Beardless Pete emerges from the gents', sees the carnage, and flees.

With his last dying effort, Ray upsets a glass, dissolving the ink on the paper such that they will never become famous, and everything reverts to them sitting in the bar before Cassie arrived.  They leave for a different pub.

There are a few games played in the last minutes of the movie, including the return of Cassie to get Ray, but they are not part of the main story.  It is as they say holier than Swiss cheese, but still a lot of fun, and offers some interesting talking points for our series ahead.

In order to put time travel events in sequence, it is necessary to work based on the order of their departure times.  The first time travel event we see is the presence of Cassie in the cozy.  She tells Ray she repairs time leaks, and has a chat with him before leaving to seek the problem into which he is about to blunder.  His superior geekery makes him more knowlegeable about temporal anomalies than she, and as he explains chaos theory and the butterfly effect, she tosses off a line which becomes very funny in retrospect, which at the time seems like she is playfully belittling the importance of what he is saying.

His point is that having come from the future to talk with him, she has delayed him such that he is now on a different schedule.  She jokes that this means he will drink his pint a bit later and the result will be that he uses the gents' a bit later, and so the entire universe will collapse.  Her joke is that it does not much matter when he goes to the bathroom; but the more subtle joke is that because Ray is late getting to the table, and because he has this extended story to tell about the girl in the cozy pretending to be a time traveler, Pete's trip to the gents' is delayed.

This is problematic, because we never understand how the time travel works in this movie--that is, we know that whenever Pete or any group including Pete enters either bathroom, he and they emerge elsewhen; but we do not know how the time of their arrival is determined.  If, though, when you emerge is in any way affected by when you enter, Pete's entrance has been advanced significantly.  Based on time markers of the film footage, Ray spends at least five minutes chatting with Cassie in the cozy and closer to six and a half (including interruptions) telling the tale once he returns to the table.  Absent Cassie, Pete would have had his drink five minutes sooner and would not have stuck to the table as long to hear the end of the story, and so almost certainly would not have entered the gents' at the right minute to travel forward to the moment of his own death.

This disrupts everything, because we cannot be certain what will happen instead.  It is possible that he will go to the gents' before the time leak begins, and they will leave the paper on the table and head for the other pub.  That is the best of all possible scenarios.  The worst is that he will fall into the time leak and emerge at some other unknown time, and will not have returned until after the guys started worrying about him, perhaps that they will search for him and also fall into the time leak, traveling separately through history.  The least likely is that he will travel forward to the same time as he would have had he not been delayed--which leads to other questions to be addressed.

It thus seems that the scenario most likely to produce a working story is that Pete goes to the gents' and returns before the time leak occurs, the trio leave the pub with the note on the table, and however it happens that note makes them famous, incidentally rich, and they never travel through time.  That means that the first trip anyone makes is the one that brings Cassie to the cozy to meet Ray and seek the leak they never found; and indeed, because she delays him for a five minute chat he returns to the table five minutes later, and tells a six and a half minute story, and Pete does not leave for the gents until Bonnie Tyler is singing Total Eclipse of the Heart.  That delay is necessary to start the rest of the adventure.

We assume that when Cassie does not delay Ray in the cozy, Pete reaches the gents before the time leak occurs and does not travel to the future.  He returns to the table, the trio gathers its stuff, leaves the letter to Hollywood on the table, and heads out to catch last orders at another pub.  All of their time travels are avoided; more properly, they did not happen in this, the original history.  They will be introduced in a subsequent timeline.

We are given very little information about the future.  We know that Cassie travels several times from some distant future to the present, and that she does so months apart.  We also know that Millie travels from the future at least twice.  (We do not know whether she travels to the fan party and from there to the present, or whether from the fan party she returns to the future and then comes to the present, but that is not at issue at the moment.)  Given, though, that Cassie is unaware of Millie's involvement and unaware that Millie is going to kill everyone in the bar, she must have come from a history in which that had not happened.  That means that Cassie must have left the future first, and left the future several times several months apart, before Millie did.  Thus the first trip to the past must have been the one in which Cassie meets Ray in the cozy, and she must make all three of the trips we see temporally prior to Millie's first trip.

Thus in a metaphysical sense the first time trip is the first one we happen to see:  Cassie leaves from an undefined future intending to repair a time leak, alters history by meeting Ray in the cozy, which delays his return to the table with the drinks and begins a new timeline in which Pete goes to the gents' later.  Because Pete went to the gents later, he gets caught in the time leak, and gets carried to the future.

This introduces our next problem.  When Pete returns to the bar, no one is dead--Millie has not yet left from the future.  Thus he will not rush back to the bathroom, and that means he will not be transported back to earlier in the evening.  He will go directly to his table, finish his drink, and suggest to his companions that they go catch last orders at the other pub.  Probably, though, his friends will wonder where he's been, and he will wonder why they wonder.  Yet if we do the math in the scenes we see:

• Total Eclipse of the Heart has run about half a minute when Pete leaves the bar; after his return it runs another half minute.  There are three versions of this song, but the radio version, most likely to be in the juke box, is four and a half minutes long, and the album version over seven.  That means at least three and a half and possibly six minutes there.
• It is about two minutes from the moment of his return to the trio entering the gents', overlapping by half a minute.
• It is not less than thirteen minutes from the moment the bartender asks if the drinks are dead to the breaking of the glass at the end of the death scene, again overlapping half a minute.

That's not sufficient for him to drag them back to the gents', so again they will leave, leaving the paper on the table, and become famous and rich, and Cassie will depart from the future to fix the time leak, meet Ray in the Cozy, and put everything into its settled order.

The tricky part is getting the next event.

In order for Pete to enter the gents' at the right time to travel to the future, Cassie must first travel from the distant future to create the delay.  Pete then catches the time leak and bounces forward about twenty minutes.  However, although the song on the juke box has changed, there is nothing sufficiently different in the bar to scare him back to the men's room, and so that's the end of the time travels for our intrepid trio.  Cassie will make her trip on schedule, and everything will fall into place--we have resolved to an N-Jump.  In order for anything else to happen, Pete must return to the gents'--which he will do only if he sees everyone dead.  Thus, Millie has to kill them, which means the next trip brings Millie from the future.  She does not have to visit the fan party, because the boys never went there; she simply travels to the bar.

Millie hits a snag:  she is here too soon.  It is simple enough to kill the two boys and leave, but she won't get the third, because he's not only not in the bar, he's not actually in the gents'.  At this particular moment, he does not exist anywhere in the world, having leapt over this time to a time still six to seven minutes in the future.  Now her problem becomes ours.  Ray and Toby are completely unsuspecting; they do not know that they are to become rich or famous.  She could kill them and leave, and then she's killed two--but not seeing a bar filled with the dead and himself on the floor, Pete will not rush back to the bathroom immediately, and will not catch the time leak the same way.  At the same time, her purpose is to kill all three, so she should wait until his return and then kill them--but if she kills them, our story ends, because they are dead and Pete cannot return to the past.

Certainly Millie's best strategy is patiently to await Pete's return, then quietly kill the trio and exit.  They would be found dead with the paper on the table that makes them famous, and that would be the end of the story.  But fortunately for the story, Millie does not appear to be a patient person.  She will kill the two who are there, and not finding Pete, will assume he must be somewhere in the building, and so kill everyone.  With everyone dead, she assumes (not aware that he has left the universe briefly) that Pete is among them, and will exit.  Pete will then emerge from the gents' to find everyone dead, but not his bearded self. He will run back to the gents' on schedule and catch the time leak back to a few minutes after his departure.  Ray does not upset the glass, because not yet having gone to the future he does not know that that paper makes them famous.

Pete's return to the "present" creates a new timeline, in which as the song ends he is telling the story of seeing everyone dead in the bar.  It is not the story he tells in the movie, because he did not see his bearded self; this sets up a conflict between a desire to leave for the other pub and a desire to be believed.

If they leave the pub, they won't be killed when Millie attacks; but they won't travel to the future, either.  Thus it must be that Pete persuades them to visit the gents' to verify his story, which takes them to the next anomaly.

Cassie changes history by delaying Pete's visit to the gents', and Pete leaps forward but no one notices, and then Millie changes history by killing everyone in the pub in a futile effort to get Pete, who at that moment is elsewhen.  Pete returns to a room full of dead people, rushes back to the gents', and travels back before the incident.  He tells his story and makes the bet, and the trio take to the time leak and travel back probably about half an hour, seeing themselves doing what they had been doing half an hour earlier, writing the letter to Hollywood.  They exit to the hall, wisely decide not to risk returning to the gents', and decide to hide in a closet to wait for their doppelgangers to fall into the same trap.

Ray then realizes that they are far enough in the past that Cassie is in the cozy, having a conversation with him.  He catches her exiting, but she does not see that there are two of him and so when he tells her of the leak in the bathroom she thinks he is ridiculing her, and storms out through the door.

In the film, she reenters through the same door immediately, six months older with different clothes and hair.  That does not happen this time; Cassie exits to some unspecified future and cannot return until that future moment is reached.  Before that happens, much must occur.

The Cassie coming from the cozy left before Millie, and is unaware of the massacre.  That will change.

The intrepid trio has no better plan than to wait in the closet for their duplicates to enter the gents'; Ray is probably a bit dejected that Cassie did not believe him, but his actions will not change from that.  Once they see their selves enter the gents', they will emerge from the closet; then Pete will again want to use the bathroom, and to avoid meeting themselves they will use the ladies, on schedule, catching the other time leak which flings them far into the future.

This visit to the future poses numerous problems for us, largely because we now have two dissociated futures--one from which Cassie and Millie travel, which judging from clothing and time travel abilities is highly technological and reasonably upscale; the other in which Ray, Toby, and Pete arrive which is a post-apocalyptic wasteland.  The problem is integrating these two worlds, and either way we encounter trouble.  Is this, on the one hand, a time long after the prosperous era of the time travelers, and if so why are the ruins of the pub here?  On the other hand, is this the earlier world, and if so how did we get from this to that prosperous future beyond?

This is an important issue to the analysis.  If Cassie and Millie come from a far flung future beyond the devastation visited by the trio, then the travels of Ray and Toby at least are contained within the timeline they created; if instead they have traveled beyond that future, then Millie and Cassie will both again leave from the future to the past before the boys reach their future end point.

The crisps are stale-dated to 2094.  The pub had to be open shortly before that to have stocked them, but closed not later than that to have kept them.  Whatever shut down the city was happening then.  It seems unlikely for the girls to come from a time before that, but problematic if they originate later.  We must determine how they could come from a post-post-apocalyptic universe.  That will be our consideration for next time.

It is a joke in the movie, which Ray makes not as a joke but as an observation when they meet Millie:  "Apparently everyone in the future?  American."  The joke of course is that so many science fiction movies and television shows are made with American actors and thus the futures they portray are filled with American accents.  Yet it may help resolve our post-apocalyptic problem.

The future which Ray, Toby, and Pete visit is clearly a post-apocalyptic disaster, filled with many of the tropes common to the genre:  collapsing infrastructure, a blanket of what might be snow or ash either falling or blowing about, everything in shades of grey but for some vile looking bright green liquid that is the nearest substance to water in sight, and the incidental presence of a giant insect that eats people.  It does not seem to be the future from which Cassie and Millie originate--and even if we place their world in a future later than this, how could humanity recover from such a low to such a high and retain knowledge of this era?

Yet as Ray observes, it could just be a bad area.

Certainly it is silly to suppose that you could look out over that landscape and think that a few miles away it's much better.  However, there are places on Earth right now which are comparable to what they see.  England is a far northern latitude, on a par with Nova Scotia and Alaska, kept warm by the Gulf Stream which carries equatorial waters north along the western coast of Europe.  A change in that current could bring about a freeze there, pushing it into Siberian conditions.  Combine that with a fuel crisis and you have uninhabitable cities and the flight of humanity to warmer places.  It is not impossible for the disaster to be localized to Northern Europe, and for the Southern United States to flourish.  Ray, Pete, and Toby are limited spatially to wherever the time leak happens to be, connected as it is to the restrooms of the pub even after the building collapses around it.  Cassie and Millie clearly are not, having time-and-space travel ability built into their bodies.  Cassie came to fix a time leak; Millie came to kill three famous people.  They could have come from anywhere in the universe.  We believe Cassie when she says she is not from space or a spaceship, and since she knows Millie that suggests they come from the same place and time.  It might be some part of the world that was not destroyed, that continued to flourish and advance even as this part decayed and collapsed.  It is a bit unusual to imagine a post-apocalyptic world that involves destruction in limited areas, but it is not impossible nor even unknown--On the Beach supposed that Australia was never touched by the bombs in the nuclear war that destroyed all the major countries of the world, although its survival was to be brief as radioactive fallout carried on trade winds was certain to finish the rest of the planet's life.

There are two problems that must be addressed.  The first will have to wait, and that is the travels of Pete in what for the others are a few seconds.  The second, though, is the mural on the outside wall of the pub.

Someone painted a portrait of the threesome sitting at the table with their famous paper, and that portrait appears both later (which is chronologically earlier) in lights at the fan party and now on the wall over the front door of the pub.  The pub clearly is capitalizing on the fame of the event which happened at one of its tables.  However, the mural as we see it has them dressed in the clothing they scrounged in that post-apocalyptic world.  That cannot exist as it appears until after they have returned to their own time.  Nor can Pete have the beard until he has returned.  Thus the mural they see will be different, probably displaying them in the clothes they were wearing when they departed, or possibly, if it was composed from photos, in other clothes.  The trio became famous because of the note they left on the table, and that note is there; in this history they never returned.  Their images would still be preserved, but they would be different images.  Eventually they do return, and because they are seen in these clothes the mural is replaced by the one we see.

Not seeing themselves in these clothes, though, they do not yet realize that it was that paper which made them famous.  There are several other problems at this point, however.

In considering the presence of the trio in the post-apocalyptic future, we said that it created several problems.  One of these is that when Millie arrives to kill them, they are not there; they are completely missing from history at that point, having stepped into the ladies' mere minutes before she arrives and so being carried perhaps a century or more into the future.

Millie cannot kill them, because they are not there.

Yet if Millie does not kill everyone in the bar, then when Pete emerges minutes after she leaves, he has no reason to return to the gents', and our trio leaves for last orders at the other pub.  They never jump back to see themselves in the past, and more critically they never enter the ladies' to leap forward to this future.  It must be that not finding her quarry, Millie kills everyone in the bar.

Does she then begin a search for her victims, intending to bring them back to this time and add them to the death toll?  This introduces an entirely new layer of complication.  It tells us that Millie, in her own sequential timeline, made the trip to the pub first, and then made the trip to the fan party (possibly making several trips in her effort to track them) to send them to the execution.  However, if she later succeeds in sending them to the execution, then her earlier self at the execution will not know that they would not be there save for her future intervention, and she will not begin the search for them.  If she does not search, though, they will not be there--and so we have an infinity loop.

We can avoid this by having Millie find the trio and return them to the bar first, and then come to kill them.  This, though, raises other problems.  First, as already seen, unless Millie makes the trip to kill everyone before Pete exits the gents' the first time, he will not return to the past or press his companions to make their first trip.  Yet she cannot look for them until she knows they are lost, and that means she has to have reason to believe that they are lost before she makes the trip to kill them.

This can be resolved, though, if we assume that Millie knows the history, and in this history the trio never returned to that moment.  That means that temporally before she leaves to kill them, she first leaves to find them, even though metaphysically before she looks for them she makes the murderous trip.  To clarify, in the original history she leaves on Friday to kill them, and kills everyone in the bar, causing Pete to run back to the past; then as history returns to that moment she realizes that the trio vanished, deduces that they are lost in time, and on Wednesday leaves to find them and restore them to the place where she can then kill them when she leaves on Friday.  Thus her Friday trip is preserved, and her earlier trip for which there is no point in the original timeline is added in the new timeline.

That creates a new problem, because once Millie restores them to the pub she cannot know they were missing.  To resolve this, she must somehow get a message to herself--setting up a sawtooth snap from the small changes which follow, but ultimately stabilizing to an N-jump.  That is a complication to which we will return.

Yes, this is getting complicated; but there's yet another complication.

The post-apocalyptic visit introduced another complication related to Pete's travels, and we've come now to address that.

Pete spent months bouncing around history, sometimes staying long in one time and sometimes moving quickly to another; we do not know more than a few fragments of this.  We know that on one occasion he stepped into the gents' and saw himself from behind threatening his companions with a butcher knife and did not recognize them; he immediately left, but when they pursued him they apparently did not exit to the same time he did.  We also know that he described stepping out the door and falling a long distance into a wood which he took for prehistoric, but stated that if that were correct there were gaps in the history.

The problem with envisioning a prehistoric trip is that it raises serious issues concerning the mode of travel.  To this point, the assumption is that there is a time leak spatially localized to the pub restrooms.  When the trio emerges in a post-apocalyptic future, they do so in the ruins of the pub through the still standing doors of those facilities.  Time inside the room is strange and overlapping in peculiar ways, but the outside of the door cannot exist prior to the construction of the pub, and therefore even if one could exit to a moment of prehistory no door would be there through which one could again enter.  It thus seems necessary that Pete must have traveled to the future.

That, though, raises another problem.  We have already concluded that England suffers a post-apocalyptic age sometime not too long after 2094, and that concurrent with that someone is developing time travel in America.  The future to which Pete travels must be after the apocalyptic age; the remains of the pub and the city itself have vanished in the primitive forest, and the ground in front of the rest room door has dropped forty feet whether by erosion or cataclysm.  We need to add more than a century beyond the time of the post-apocalyptic world.  At the same time, if Pete travels to a point in time subsequent to the world of Cassie and Millie, their anomalies are then contained within his and must be resolved before he can reach that future point.  Yet Millie's objective involves finding and killing them in their own time.  That creates a problem, and brings us to yet another problem.  It is evident that absent Pete's return, Toby and Ray will return to the ladies'; Pete will not be there, and when they exit they might be in yet another time.  That leads to another question concerning the nature of the leak.

The most plausible consequence is that the duo is thrown into their own temporal excursions, creating more anomalies.  In the centuries they explore they never cross paths with Pete.  Ultimately when Pete pops out of the gents' and stops them, he erases all that history.  He can do this with impunity because he knows nothing of that history and it is not his intention to erase it, and we are fairly certain that nothing the duo does impacts what Pete does.

The other possibility, though, is that the time travel does not work for them.

Cassie and Millie have time machines built into their bones.  Ray, Toby, and Pete travel by accident, because there is a time leak and whenever they enter either bathroom they stumble out in another time.  Yet at least one other person--an elderly man--enters the bathroom at least one time, and apparently is not so affected.  In fact, no one ever travels through time by entering the bathroom unless they enter and leave with Pete.  He is the only person who travels alone, and his two friends never travel save with him.

If this is the case, Ray and Toby will burst back into the ladies', probably finding it as ruined as the rest of the pub.  They will also try the gents', which will be similarly decaying.  They will eke out survival in that future world, and ultimately they will die, because without Pete and without help from Cassie or Millie, they cannot leave that time.

It is not clear whether Cassie or Millie could help them.  At no point does either take anyone through time; their time travel powers might be limited to single individual use.  (The portal at the end is specifically said to connect to a parallel universe, so that does not count.)  Millie is able to direct the trio such that they enter the gents' at the right moment to exit in their own time (if a bit early), but she uses the time leak to move them.

What happens to Toby and Ray is thus important, and it could upset events drastically; however, ultimately Pete happens back at the perfect moment to undo all of it, and no one knows what originally happened because now it never did.

Pete's return undoes whatever happened to Ray and Toby, and now the trio scrounge clothes, arm themselves, and resume their temporal quest.  However, two things now happen in the men's room.  First, they hear themselves entering, and hide in the last stall, narrowly avoiding interacting with themselves.  Second, while they are arguing, a younger Pete enters, sees them arguing, and flees.

The first event is interesting for what might have happened:  had Pete warned them against entering the ladies', they would not have traveled to the post-apocalyptic future and would not be here now to warn themselves--an infinity loop.  On the other hand, interference with the timing is itself problematic.  We expect that the destination point is somehow determined by the moment of departure, that is, if you stay another minute you wind up elsewhen.  Thus had Pete warned the threesome against entering the ladies', they would have left the gents' at a different moment, not half an hour before they entered but at some unpredictable other time.

That did not happen then; but it might have happened with the other encounter.  While Pete has his back to the door and is threatening Toby and Ray, both of whom are oddly dressed wearing hoodies which help obscure their identities, the Pete who has been petering about through time enters behind him.  He sees a man with a knife threatening two men in hoodies, and immediately exits.

Toby picks up on this, because Pete mentioned having seen them when they donned their clothes in the future; but of course, he didn't in this history, because he did not see them until after they had doubled back and crossed paths with him there.  That also means that on this particular entrance, he left the loo sooner than he would have done, that is, than he did in the original history.  That in turn means that he changes his path through time, going to different times thereafter.  Again we have the implausibility that one of these trips takes him to exactly the right moment to prevent Ray and Toby from returning to the ladies'--implausible because not only is that a very narrow target time in the history of the world, but he hits it coming along two different paths.

Or perhaps how long you stay or when you leave is irrelevant to your point of arrival.  After all, the trio pursue the other Pete as he flees the gents', and wind up at the fan party where he apparently did not go.  The juxtaposition of the seemingly capricious nature of the time travel against the seemingly established arrival points is one more oddity here, but since the film never attempts to explain why anything happens the way it does it is difficult to say when what happens is inconsistent with its own theories.

The first time the boys reach the party, they are dressed in the peculiar attire they donned during their time travels--but the fans are not.  Just as the mural could not show them in these clothes before they returned to their own time to be seen in them, so, too, their images at the party will be of the normal selves who never traveled to the future.  That also means that it's less likely that there would be a look-alike contest.  A significant part of the inspiration of such a contest would be the peculiar dress the threesome wore that night, causing them to stand out from the crowd.  It is unlikely that there would be a look-alike contest for three relatively ordinary looking nerds (pardon me, imagineers) in relatively ordinary clothes.

There still might be a fan party; it's just that the three people who are the objects of adulaton would probably pass unrecognized, even perhaps snubbed for their odd clothes.

This is where Millie finds them.  Whether by some special knowledge of time or some tampering with the leak, she sends them back to the pub so they will be there when she arrives to kill them.  What is curious, though, is that she finds them.  One of three things must be true:

1. The threesome's appearance at the party was recognized by someone, and reported to some historic record which Millie found.  This seems improbable.  They were not recognized when we see them, they are not dressed in what would have been their normal clothes, and they are trying not to be recognized.
2. Millie has some method of tracking time travelers.  If this were true, however, she would have tracked them to the post-apocalyptic world.  They were there for an extended time, they were alone, and if you're following the trail from the starting point you get there first.
3. Millie wandered through time until she stumbled on them.  This seems improbable, given how much of time there is and how little of it the trio visited together, but possibly the nature of the time leak limits the number of possible temporal locations, or possibly she got very lucky.

There might be some combination of the second and third options at work here.  However, there is yet another problem.  Before Millie can find them at the party, she has to leave from the future to seek them.  This means all the intervening time between when they reach the party and she leaves the future must pass.  Again, we have three possible scenarios:

1. They re-enter the gents' on schedule and return to their own time.  If, though, they did this, that would rewrite history such that they were present when Millie killed them, and she would never know to seek them.
2. They re-enter at a different time and go elsewhen, continuing to create anomalies until they accidentally return (giving us the first scenario), or they die somewhen, or they travel to a future beyond Millie, which means she has the opportunity to leave and find them.
3. They decide to stay when they are, establish their true identities, and enjoy their fame, if not their fortunes.  That would put them in the history books so Millie could find them.

Having found them at the party, Millie sends them back to their starting point, or very nearly so.  For a brief time, there are three sets of them in the bar, each trying to avoid their earlier counterparts.  Gradually it thins, prior versions of themselves catching their own temporal hops to other times, until they reach the table.

A very peculiar point has to be made now.  Millie is about to arrive and kill everyone in the bar.  However, the two things which warn Ray of this have not yet happened.  The one is that Cassie is going to make another trip from the future to tell him everything is fine, and the other is that he has realized that they are famous because of that note on the table.  This means that when Millie returns and kills everyone in the bar, Ray knows that it's because they were famous, but he does not know why; and not knowing why, he cannot recognize that paper as the reason for it all.  That means he does not destroy the paper--which is essential to the story, because in order for the fan party to occur as we see it there must be a history in which the threesome become famous in those clothes.  If Ray destroys the note, that history never exists even to be undone.  He has no way of knowing that the note matters, and no way of anticipating Millie's death stroke.

This sets up a new history, which we will attempt to reconstruct next time.

What makes the film so convoluted is the sheer number of trips to the past, each one of which alters the past requiring that all of the history from the arrival time forward be rewritten.  Our original history ended when Cassie left seeking a time leak and delayed Ray so that Pete was late reaching the gents' and was carried forward a short hop.  That stabilized, Cassie making the same trip.  Then Millie visited the past, killing everyone in the bar, but not Pete, who saw the carnage and returned to the gents.  This leapt him back for a short anomaly, in which he persuades Ray and Toby to enter the gents', which creates yet another anomaly as they arrive earlier in the evening and avoid themselves.  They wait as Cassie arrives and departs, as Pete leaves and returns, and as their counterparts enter the gents'.  Then they enter the ladies', and leap forward at least a century.

In that time, Millie kills everyone in the bar, Pete leaves and bounces around a bit then returns, and the trio travels back to the party.  Perhaps they stay there, not quite in their own time but close enough, dying in the future.  Millie leaps back to find them, and sends them to meet the massacre.  They die, but become famous.  Their younger selves are already in the future, but now the mural has them in these scrounged clothes, and they have their clue:  that paper made them famous.

This time, when they reach the party everyone is dressed like them.  Millie arrives and sends them home, where she will kill them on her next trip to the past which she has already made.

Because Millie found the boys at the party, she can send a message to herself to seek them there.  This has the least impact if she originally found them based on history rather than searching, although it does change her own history slightly; she can still send herself the same information and so make the same trip.

However, we are overlooking someone.

It quickly became apparent that Cassie made the first time trip, because that delayed Pete and hopped him to the future.  It then had to be so that Millie was next, because without her massacre Pete stays in the future.  Cassie appears twice more in the film, but it is not at all clear how she can do so.  Of particular complication is that she comes from the future, but is not aware that Millie kills the boys in the pub that night.  We need a timeline in which the boys become famous and Cassie does not know they were killed.

Fortunately, we have one, and it helps us organize the future end events.

In our analysis, we noted that when the boys reach the fan party, they could opt to stay, attempting to reclaim their lives with the temporal gap.  We don't know how long they have been gone, or where their wealth went, but we presume they had family, and we know that it is less than a century (the film was made and presumably set in 2008 and the pub is closed by 2094).  We have also concluded that Cassie left, from America, some time not too long after that, and that she left before Millie both chronologically and metaphysically.  In this history, there was a massacre in the pub; but since Ray, Toby, and Pete never returned to it there is no reason for Cassie to know that they were the target, or perhaps even that it occurred.  Thus all that has to happen is when Cassie returns to her own time, she makes her additional trips from the timeline in which the boys stayed at the party, before Millie makes her own trip to return them to the massacre.

Thus the threesome stayed in the future, died presumably peacefully in the future, and since they had made a relatively short hop Cassie is unaware that they made that trip.  Ray, having just from his perspective made his first time trip back half an hour, catches her on her first visit to his time, tells her that the leak is in the gents', and she storms out; but then she spends six months tracking the leak and finds it in the gents, realizes he was not lying, and comes back to apologize.  She is still unaware that he lived as long as he did because he skipped a few years, but she assures him everything has been fixed.

That's a peculiar point, though, because not everything has been fixed.  On the other hand, what would happen if it were?  Indeed, what would it even mean?  Supposing that at ten o'clock they stepped into the gents' and leapt back to nine, the leak would have been there at ten.  If Cassie travels from the future and repairs it, then the leak is not there at ten, and when they enter the gents' they don't go anywhen; but then they aren't hiding in the broom closet because they didn't make the trip.  So perhaps she can only fix it at a moment after they make that trip.  This, too, makes no sense--either she can change the past by making it so that the leak did not exist, or there is nothing she can do about the leak which will exist for as long as it does.  In any case, since Pete travels to distant times, and the trio return via the gents', that leak spans centuries, one way or another.  If the leak were fixed, it would prevent them from making the trips they make, changing history yet again.

Assuming, though, that Cassie leaves from the future twice more before Millie manages to return them to the pub to be killed, on her third trip the boys are not there.  She does not spend several minutes talking with Ray outside, and she does not return to the pub to be present when the attack happens.  This could be serious--but that she has no reason to expect them to be there, rather than to have left for a different pub.  She writes it off to her bad luck.

Then Millie makes the trip by which she returns the boys to the pub; and since she is already there to kill them, that becomes history.  That means we expect a timeline in which Cassie ought to know that Ray died there that night.  However, since that change happens before her departure point, there will be a version of her unaware of Ray's death.  History must again reach her departure point for her to know this--and perhaps it never will.

Everything has been working toward the confrontation in the pub.  For that to happen, though:

1. The trio must know that the paper makes them famous.
2. Millie must restore them to their proper time.
3. Cassie must make her third trip, telling Ray Millie is an editor.

Millie exits; Pete enters.  Ray is dying, but in trying to destroy the paper he knocks over a glass.  Pete flees, returning to the past, and the beer in the glass obliterates the writing on the page.

Arrivals whose departures have not yet been replaced still occur on schedule.  Pete can arrive and return; Cassie can be in the cozy.  The trio make their backstep, then get thrown forward.  However, they now will not be famous, so there will be no mural, and no fan party.  Millie still meets them then and directs them home.  Cassie arrives, and tells Ray that Millie is an editor--but this Ray is missing one of the pieces:  he does not know why he is famous.  He does not know the paper matters--unless Millie tells him.

If she does not tell him, he does not destroy the paper.  That makes him famous, restores the mural, and so gives him the clue to identify the paper.  In that case he will destroy it, erase the clue, and put the world in a very convoluted infinity loop.

If she does tell him, he will attempt to destroy the paper.  If he does not succeed, we have the same infinity loop.  However, if he does, this anomaly stabilizes, as he is not famous, does not get the clue and does not destroy the paper.  History then advances to the moment Cassie leaves for her first trip.

Cassie still comes to the pub seeking the time leak.  However, Ray is not famous, so she will not stop him in the cozy.  He reaches the table five minutes earlier, does not tell his story, and once Pete goes to the gents before the time leak, they head for another pub, leaving the paper on the table.  That makes them famous, bringing Cassie to the cozy, and we have another infinity loop.

In the end, it's simple.  Ray will only destroy the paper if he becomes famous; he will only become famous if he does not destroy the paper.  These two versions of history alternate perpetually, trapping time forever.

Several things happen after Ray destroys the paper.

If Ray destroys the paper, we revert to a history in which they finish their drinks and leave to catch last orders elsewhere, just as we see in the movie.  However, none of their adventures happened, so they don't remember them, and are not discussing them.

We see Cassie arrive through an interdimensional portal.  Since Ray was never famous and Cassie never met him, she shouldn't do that.  On the other hand, there are several other ridiculous notions, as she tells Ray they have been a couple for a long time and he is not aware of this and has done nothing since not meeting her at the bar.  Perhaps, though, there is another temporal problem.  After all, we noticed that the time leak is connected to Pete, so perhaps he is temporally unstable in a way that creates another leak.  Why Cassie would come get an earlier version of Ray is entirely guesswork, but not an impossibility.

Multiple versions of the boys are then seen interacting with each other.  This is not impossible, as temporal duplicates have already occurred in the film--three of each of them were in the bar together for a while.  Exactly what sort of convoluted travels would have this result is difficult to guess, but it could happen.

The notion that the portal goes to another dimension raises many questions about parallel and divergent dimensions, but the film does not explore them, and the time travel we see is clearly all in one universe.

There are questions unresolved, particularly regarding what happened when in the future.  Did Cassie leave first, or Millie?  Do they come from a nearer or more distant future than the post-apocalyptic one?  Our reconstruction makes everything work as well as we are able, but there might be other options overlooked.  Overall, though, it is a fun and convoluted story that ends in temporal disaster.