British politics quite often feels like an unpleasant hangover, but Labour and the Conservatives will be fully justified in spending today in bed: last night they both got absolutely hammered.

Although, at the time of writing, several council votes remain undeclared, it is clear the local elections delivered a nasty plague on both parties’ houses. The Conservatives are forecast to shed hundreds of seats, while Labour, which was predicted to make significant gains, has actually lost some councils. Local elections can vary in importance, but this could be the gust which presages a far greater storm. The last few weeks have set down the possible conditions for the collapse of the country’s two main political parties.

The problem is both are paralysed. The cause is Brexit. Leavers are furious with the Tories for negotiating a poor deal and extending the Article 50 process, and furious with Labour for countenancing a second referendum. Remainers are furious with the Tories for selling them out and ignoring the economy, and furious with Labour for continuing the fantasy of a “jobs-first Brexit” and not explicitly committing to a new vote. Meanwhile voters in the middle are enraged by the endemic failure they perceive across the political establishment, and wish to punish both its principal protagonists.

The key agony for the Conservatives, besides boasting the worst prime minister in modern British history, is that they believed their own hype for so long they can no longer unbelieve it. Five years ago Brexit more or less meant a Norway option, and it was perfectly plausible to envisage a common external tariff. But fanaticism and mission creep have long since subsumed both proposals into the narrative of betrayal, while a second referendum would apparently represent treason by voters against themselves. Unfortunately, the Tory leadership is beginning to understand that Brexit cannot be delivered in the current House of Commons without the promise of either a customs union or a second referendum. They also realise the electorate might eviscerate them if they called a general election. Consequently the party looks doomed.

The Labour Party deserves far greater sympathy. It never wanted Brexit and its membership still doesn’t. For three years the party has managed a politically brilliant triangulation strategy, carefully navigating a channel between Leavers and Remainers designed to placate both. That strategy was delivered through nudges and winks, with the two camps proffering alternative spokespeople who sounded different enough to keep their own wings happy but similar enough to keep the party policy intact. There was no need for resolute clarity while the government was destroying itself, and party grandees knew they had to withhold that clarity until the last possible moment. The problem for Labour is that the moment has arrived and now passed.

This week’s meeting of Labour’s National Executive Committee (NEC) was the party’s opportunity to clarify its Brexit policy. Following on from the successful conference compromise, which pledged to support a referendum if the party could not force either its version of Brexit or a general election, leading Remainers wished to introduce the next prescribed stage: to declare a referendum the condition for any deal. In the end, the NEC stuck with the compromise wording and refused any unequivocal commitment to a new vote.

This was not just bad policy but bad politics. Labour has now been inching towards a second referendum for months. Jeremy Corbyn whipped for it twice in the indicative votes, and if the government refuses to countenance a customs union acceptable to Labour, the party will have to whip for it again. The problem was that it didn’t feel able to make that destination clear for fear of upsetting Labour Leavers—and this was its fundamental error.

Labour Leavers who prioritise socialism will vote Labour whatever it decides on Brexit. Labour Leavers who prioritise Brexit (a minority, according to polls) will never vote for a party that even contemplates a referendum. The most hardline will not even back a customs union, which forms the plank of Labour policy. In other words: a key tranche have already left and will not come back. The risk is that Labour Remainers will now follow them.

Labour Leavers have no end of alternatives to choose from: the Tories, Ukip or Nigel Farage’s new Brexit Party. Meanwhile Remainers can opt for the Greens, Liberal Democrats or newly-minted Change UK. Although the Brexit Party and Change UK were not contesting the local elections, Labour lost numerous seats to the other Remain parties. After nine years in opposition, at a moment of national breakdown, the party should be preparing for government. Instead it is losing support. In politics it is impossible to please everyone, but entirely possible to alienate them. The European elections on 23rd May and Peterborough by-election on 6th June, in which Labour will defend a majority of 607, could drive the point home.

The only thing worse than bad results is bad interpretations. Labour MPs could misread a poor showing in the local or European elections as an instruction to support May’s deal and prop up the government. This morning there have already been murmurs of disquiet from some MPs in Leave seats which lost Labour councillors. But the problem is not that Labour is insufficiently pro-Brexit; it is that the party cannot fundamentally be pro and anti-Brexit at the same time. And because Labour can never be more pro-Brexit than the Tories, it must be more openly pro-Remain.

But if Labour instead chooses to “bail the Tories out,” in the words of Shadow Trade Secretary Barry Gardiner, the party could find itself the Tories’ new saviour and a Tory Brexit’s new midwife. Such a move would drive Leavers and Remainers from both parties and potentially split each down the middle. It could prove the greatest combustion and recalibration of British politics since the 19th century.

The Conservative and Labour parties are presently caught in a standoff. While their peripheral support drains away, first they will stagnate, then they could sink. Neither party can win any election on its core vote alone. The divisions in the country are less political than they are cultural. Left and right have submitted to Leave and Remain. Brexit has changed everything it encounters, and there is no reason why our party system should prove exempt.

And so while bleary-eyed pundits today try to make sense of what happened last night, they should remember the real hangover is from 23rd June 2016. It will be making us sick for many years to come.