Theresa May's successor will be chosen when the Conservative Party holds a leadership contest after 7 June, when she will become an official caretaker prime minister.
Boris Johnson is now the odds-on favourite to replace her and Johnson, as well as all the other leading contenders — Dominic Raab, Michael Gove and Andrea Leadsom — are more hawkish on Brexit than May, who had actually campaigned for Remain during the 2016 referendum.
Silvia Dall'Angelo, senior economist at Hermes Investment Management, told the BBC she believed the next leader of the Conservative Party would come from the "intransigent Eurosceptic wing" and the stalemate in Parliament could only be broken by an early general election.
The Tories are expected to have suffered a drubbing in Thursday's European elections — the results of which will be announced on Sunday night — and May's resignation on Friday was partly based on the assumption Nigel Farage's Brexit Party will have made massive gains at the Tories' expense.
— Boris Johnson (@BorisJohnson) May 24, 2019
That was in a fairly pointless European election — the elected MEPs will probably only sit in the Parliament in Brussels for a few months — but the worry for most Conservative MPs is what would happen in a general election if the party does not change its policy.
— Larry the Cat (@Number10cat) May 24, 2019
The University of Kent has done modelling of a general election and found many Tory MPs — including Boris Johnson in Uxbridge and Amber Rudd in Hastings — would lose their seats to Labour, as the Brexit Party takes voters away from the Tories.
Professor Matthew Goodwin, from the University of Kent, told the Daily Telegraph the Brexit Party was mainly gaining votes from "disillusioned Tories" and said: "Even if Nigel Farage and his new party get anywhere near what UKIP achieved in 2015 then it is game over for the Conservative Party."
But if Boris Johnson or another Brexiteer wins the leadership contest at the end of July they are likely to ditch Theresa May's deal — which has been rejected three times by Parliament — and copying the Brexit Party by supporting a no-deal Brexit.
— Lewis Goodall (@lewis_goodall) May 24, 2019
With Parliament having already ruled out a hard Brexit, the only option for the new Prime Minister would be to call a snap general election, possibly in early September.
The Conservatives would effectively be making the general election a second referendum and be hoping that, by offering a no-deal Brexit, they would win votes not just from the Tory hardcore but also from traditional Labour voters who want Brexit more than any other policy.
Labour would be forced into reverting into a more Remain position — for example ruling out leaving the EU altogether — or to try and persuade the electorate that Jeremy Corbyn, John McDonnell and Keir Starmer could go back to Europe and ask to start the negotiations all over again.
Considering the levels of apathy and scepticism towards politicians in the UK at the moment, that is unlikely to lead to a Labour landslide.
— Sebastian Payne (@SebastianEPayne) May 24, 2019
Under the Fixed Terms Parliament Act 2011 there is not due to be another general election until June 2022, but with Parliament deadlocked on Brexit and Corbyn having been on record as having demanded a general election, it is not difficult to imagine a Brexiteer-dominated Tory Party forcing through the required vote to bypass the act and call a snap election.
Who would win it is an entirely different question.
— James Melville (@JamesMelville) May 24, 2019
May called a snap election in 2017, thinking she could take advantage of Corbyn's weakness in the polls and increase her majority. But she did the exact opposite.
Health Secretary Matt Hancock, who is also expected to run for the leadership, told the Telegraph last week: "I think a general election before we've delivered Brexit would be a disaster. People don't want it….We need to take responsibility for delivering on the referendum result."
2019 promises to be an interesting political year.