With apologies for the slight delay (European elections intervened), welcome to the Guardian’s weekly Brexit briefing, trying to make sense of the nonsensical since June 2016. If you would like to receive this as a weekly email, please sign up here. And you can catch our monthly Brexit Means podcast here.

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It was, to coin a phrase, quite a week. Theresa May’s final attempt to patch together a majority for her Brexit deal backfired spectacularly after MPs from all sides, including Conservatives who backed it last time, rejected a 10-point “new deal” that included the offer of a parliamentary vote on a second referendum.

Mounting Tory pressure for the prime minister to resign culminated in the dramatic departure of Andrea Leadsom. The leader of the House of Commons quit the cabinet amid a widespread and furious backlash against May’s proposals, saying she no longer believed its approach would “deliver on the referendum result”.

About 36 hours later, after the UK had voted in the European elections in which it had not expected to take part, May said she would step down as Conservative leader on 7 June. It had been “the honour of my life” to serve as Britain’s second female prime minister, she said, but she deeply regretted being “unable to deliver Brexit”.

May’s farewell instantly kicked off a scramble to succeed her as party leader and prime minister, a process that will be decided by Tory MPs and members and is unlikely to be over before late July. Boris Johnson was fast out of the blocks, insisting the UK must leave the EU on 31 October “deal or no deal”.

EU leaders greeted the not unexpected news from Britain by saying they were preparing for a “different breed” of Brexiter to replace May, but whoever it was should not expect the withdrawal agreement to be re-opened. France’s president, Emmanuel Macron, said he wanted to avoid Brexit “polluting” the EU after 31 October, and European leaders needed to know when the UK would go.

Business leaders, meanwhile, stressed that the next prime minister must table an urgent plan to break the Brexit impasse, amid mounting concern that candidates in the leadership contest would back a no-deal withdrawal in a destructive bout of “winner takes all politics”.

Johnson is the favourite among party members, but will face competition from as many as 20 rivals and may not make it to the shortlist of two selected by Conservative MPs: moderate Tories alarmed at the prospect of him leading the country to a no-deal Brexit rapidly launched a “Stop Boris” campaign.

Senior Conservatives including the chancellor, Philip Hammond, warned the former foreign secretary and other hardline candidates, including the former Brexit secretary Dominic Raab, that any prime minister backing a no-deal Brexit would be brought down, triggering a general election.

There’s a rundown of the favourites to succeed May here, and a look at their various stances on Brexit here (although some have since clarified their positions somewhat: Jeremy Hunt now believes a no-deal Brexit would be “political suicide”.)

Adding spice to the proceedings were the results of the European poll. As predicted, Nigel Farage’s Brexit party and the resurgent Liberal Democrats combined to ensure a calamitous night for both Conservatives and Labour.

Final results showed the Brexit party gained 29 seats, with the Lib Dems second on 16 seats. Labour held on to 10, the Greens seized seven, and the Tories finished in fifth place with just four seats. What this tells us about how the UK now feels about Brexit is complicated, but despite Farage’s win, support for pro-remain parties eclipsed that for hard-Brexit parties.

All of this prompted much soul-searching at the top of Labour and the Conservatives. Faced with an exodus of its voters to remain parties, senior Labour figures, including the deputy leader, Tom Watson, said the party must now back a second referendum – and Jeremy Corbyn eventually pledged to support a public vote on any Brexit deal.

What next

The Tory leadership contest, dominated by Brexit, officially kicks off on 10 June and should be over by mid-July, allowing the new leader time to put a new cabinet in place and set out their plans.

Candidates will have to show their stance is tough enough to impress the overwhelmingly pro-Brexit Conservative membership and see off the clear and present electoral threat of Farage’s party.

That make no deal more probable. The EU27 will not re-open the withdrawal agreement or ditch the Irish backstop, so Brexiters will hope that, fresh from the humiliation of the European elections, Conservatives would swing behind a no-deal exit, previously rejected by parliament.

If MPs did block no deal again, an election or new referendum would be the likely consequence. That means Brexit could, in theory, still be stopped – either by a Labour-led government, under pressure from Liberal Democrat and/or SNP backers, calling a second vote, or by a very different House of Commons voting to revoke article 50.

Quite how all that fits in with Britain’s scheduled departure from the EU on 31 October, however, nobody knows. Jean-Claude Juncker believes another extension is inevitable, but some powerful figures in the EU27 do not agree.

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Jonathan Freedland in the Guardian argues that it is now a fight to the finish between a no-deal Brexit and remain:

The battlefield is shifting towards a starker, binary clash of no deal versus remain. That means pro-Europeans will have their work cut out. This is the argument to press: that there is no mandate for a no-deal Brexit, a scenario that was not even countenanced, let alone approved, in the 2016 referendum. If a new Tory prime minister wants to exit that way, he or she will need fresh public consent. That could be a new public vote or a general election, although it’s hard to imagine the Tory leader eager to face the country with Brexit still undone. Which is why campaigners for a second referendum believe that all roads still lead back to them: even Brexiters, they say, will eventually conclude that a public vote is the only way to break the impasse. Perhaps this will be the endgame, a referendum offering two final options: no deal, or no Brexit.

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Owen Jones draws his conclusions from Labour’s European election debacle: