here's a breakdown of how it all happened, just in case anyone's interested. here's the tale of how Grate Britane Died Forever
2010: the conservative party aren't quite popular enough to gain total power. they team up with the lib dems to create the fusion form, Condem, and with their votes combined (it's slightly more complicated than this but it's not worth going into detail) they have over 50% of the vote, and are therefore able to do whatever they want as long as they can both agree on it.
2010-2015: the conservatives do their best to ruin everything. the lib dems block most of it except for raising university fees by 300% in exchange for a vote on a more representative voting system (people vote against it because they're told fairer voting systems are for chumps). scotland votes on whether or not to leave britain, and decides to stay after promises of more power and political agency. as soon as the vote is declared, everyone starts talking about how to give england more power instead.
2015: the conservative leader, david cameron, fearing he might not gain enough votes to form Condem this time, promises to put the membership of the european union up for a public vote because it's an emotive issue that old people (the target audience of the conservatives), who wont live long enough to deal with the ramifications of leaving, have really strong opinions about.
in the universe where his plan worked, the promise boosts the votes his party gets and he teams up with the lib dems again. they block him from running the vote because why would you trust the general public with something so abstract and important, and everything is fine.
in our universe, everyone hates the lib dems over the university fees thing now, and the promise of a european union vote makes enough people vote conservative to give them the majority. david cameron is now legally obligated to put this up for debate. he wasn't expecting this and didn't want this.
19XX: david cameron fucks a dead pig
2016: britain's membership of the european union is put up for a vote. on the "remain in eu" side, youve got almost every politician and expert warning of recessions and loss of trade deals and the eventual Death Of Britain. on the leave side, youve got a campaign thats basically "foreigners might steal your jobs, lets Take Are Country Back" and politicians using the vote as a way to grab power yelling "dont listen to the experts, what do they know? dont listen to the facts and figures, listen to your heart" and a neonazi who literally shot and stabbed a politician to death for backing the EU and doing aid work in syria.
the polls suggest the vote will be split 52% / 48% in favour of remaining in the eu because people love the status quo.
however enough people voted to leave the eu as an act of rebellion against david cameron, for the epic bantz, and because they hate foreign people, that it tilted the vote the other way and now we're 52% in favour of leaving.
scotland and northern ireland, however, mostly voted in favour of remaining in the eu, and don't want to be dragged out by england and wales. therefore, they're gonna hold another independence referendum, and will probably have to put up borders to block free movement between themselves and england/wales.
david cameron, realising his legacy is no longer "fucked a dead pig" but is now "destroyed britain for the sake of one more year in power and fucked a dead pig", resigns. donald trump, who just happened to be passing through, congratulates britain on making the right choice. the people in charge of the leave campaign realise none of them actually planned for this eventuality. the £ fuckin plummets. everything is terrible. send help.
the referendum's not legally binding, so any politician could just say "actually, yall are fuckin wrong, and we're staying in the eu", but that would be political suicide. however, presiding over the death of britain would also be political suicide so nobody knows what's gonna happen now. fun times.