Things will have to move fast if the new PM is to take the UK out of the EU before 31 October

Deal or no deal: what next for Brexit, the Tories and the country?

Now that Theresa May has announced her resignation date, what happens next?

Initially nothing. She will remain in post to bear the burden of the European election results, which will be announced on Sunday night and are widely expected to be grim for the Tory party.

She will also greet Donald Trump when he visits and stand alongside the US president and other world leaders for the D-day commemorations in Portsmouth on 5 June.

The jostling among potential successors that has already been going on for weeks will intensify dramatically. The contest officially begins on 10 June, when candidates will be asked to declare themselves formally. MPs will then whittle them down in a series of votes by the end of June, leaving party members to make the final choice.

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The party is aiming for the process to be complete by mid-July, in time for a new prime minister to take over before parliament’s summer break.

What does May’s departure mean for Brexit?

The main reason for the relatively quickfire contest is to give the new leader time to put a new cabinet in place and set out their stall on Brexit. Britain’s deadline for leaving the EU is 31 October, which leaves little time for discussions with EU27 leaders.

Brexit is likely to dominate the leadership contest. Candidates will have to compete to show their stance is tough enough to impress the leave-leaning Conservative membership and see off the threat from Nigel Farage’s Brexit party.

Boris Johnson, the frontrunner, has already said Britain must leave the EU on 31 October, deal or no deal, but he risks being outflanked on the right by Dominic Raab, the former Brexit secretary.

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The European Research Group’s Steve Baker, who voted against May’s withdrawal agreement all three times, unlike Johnson and Raab, has also said he is considering standing.

Are we on the road to no deal?

It certainly looks a lot more likely than it did at the start of the week. Champions of Johnson and Raab hope they might convince the EU27 to offer a much looser relationship, based around a Canada-style free-trade deal and, crucially, to ditch the backstop.

Failing that, they could try to take Britain out without a deal. There has not been a majority for that approach in parliament, but the hard Brexiters believe a strong showing by Farage’s party will shift the balance. Certainly, backbenchers who masterminded the last parliamentary manoeuvres to block no deal, including Nick Boles and Yvette Cooper, doubt whether they would be able to do so again.

If parliament did move against no deal, the new leader could call a general election, or even a referendum, in a bid to win a strong public mandate.

Is Theresa May’s deal dead?

Not completely. Much of the exit deal she negotiated, on issues such as citizens’ rights, the divorce bill and access to EU institutions, is likely to remain in place whatever comes next.

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She could even try to hold votes on some of its less contentious elements in her remaining few weeks in office, so that at least some of the legislative groundwork for leaving on time on 31 October is done.

Many Brexiters, however, are determined to kill the backstop. May always insisted it simply formalised the UK’s obligations to protect the open border in Northern Ireland, but Johnson and others fear it will become the basis of the future trading relationship.

The “Chequers deal”, May’s painstaking attempt to marry the needs of Britain’s economy with her Brexit red lines, looks like ancient history, though some observers believe Johnson might soften on Brexit somewhat once the leadership election is out of the way.

Could Brexit still be stopped?

Yes. A general election could return a Labour, or Labour-led government, but if Jeremy Corbyn’s party entered a coalition with the anti-Brexit Scottish National party or Liberal Democrats, it would come under intense pressure to call another Brexit referendum.

With parliamentary and public debate becoming ever more polarised, there is also a growing chorus of calls for article 50 simply to be revoked. That looks impossible in the current parliament, but some ministers believe MPs would prefer it to no deal and a general election could change the complexion of the Commons dramatically – or, of course, leave it all but unchanged.