Theresa May will face increasing pressure from Eurosceptics to stand down after accepting a delay to leaving the EU until the end of October, the former Brexit secretary David Davis has said.

Davis, who has not ruled out standing to replace her, said on Thursday that calls for her to go would rise “dramatically” but did not sound convinced they could persuade her to resign of her own accord or be able to force her out.

The prime minister cannot officially be subject to another party leadership challenge until December – a year after seeing off the last one – but a string of Conservative MPs are considering ways to show she has lost the confidence of her party.

Conservative sources were adamant that May wants to stay on to complete the first phase of leaving, which is now extended for another six months until 31 October, unless her deal passes before then.

However, a soft-Brexit deal with Labour, or a dire performance in the local elections, could be the tipping point for a coup. The problem for the rebels would now be that six months is a tight timetable for a leadership contest and a new prime minister to reset Brexit policy or call a general election before 31 October.

Davis told the BBC’s Radio 4 Today programme: “She said, and No 10 put the date of 22 May on it. When PMs put a date on their own departure, it becomes a self-fulfilling prophecy … The pressure on her to go will increase dramatically, I suspect now. Whether it comes to anything, who knows? The rules are the rules. There will be pressure on her to go, there will a new leader and then a reset in the negotiations.”

He said it would be difficult to see how May could continue to be leader until the party conference in the autumn.

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At the same time, Davis joined other senior Eurosceptics and the Democratic Unionist party in urging the UK to go back to Brussels to renegotiate the controversial Irish backstop that they fear could trap Britain into an indefinite customs union. He insisted the EU could be persuaded to reopen the withdrawal agreement despite repeated and vehement insistence to the contrary in Brussels.

Arlene Foster, the DUP leader, and the former Conservative leader Iain Duncan Smith are mounting their own mission to Brussels on Thursday to see if they can get Michel Barnier, the EU chief negotiator, to budge.

Facebook Twitter Pinterest David Davis has not ruled out standing to replace Theresa May. Photograph: Henry Nicholls/Reuters

Brexit supporters who voted for May’s deal were despondent at the delay. Andrew Percy, a Conservative MP involved in the loyalist Brexit Delivery Group, said: “The strategy of remainers who have never wanted to implement Brexit has been to vote everything down and play for time. They know a long delay probably kills Brexit and the truth is they are probably right and have probably killed Brexit.”

On the other side, those pushing for a softer Brexit compromise with Labour were cheered, along with campaigners for a second referendum, who believe the delay will give more time to build the case for another vote and hold one.

Ken Clarke, the pro-EU Conservative former chancellor, welcomed the chance to strike a deal “certainly having a customs union and elements of the single market as well”, adding that “British business would breathe a sigh of relief” if that were to happen.

In contrast, Stephen Gethins, the SNP Europe spokesman, called for May to use the breathing space afforded by the extension to hold a second referendum.



“This is a watershed moment in the Brexit process,” he said. “With the European Union agreeing to a further extension to article 50, Theresa May must use this time to hold a fresh EU referendum with the option to remain on the ballot paper.”

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Tom Brake, a Liberal Democrat MP and Brexit spokesman for the party, said: “The British people have been given a lifeline. The Conservatives have dragged the country into chaos, but the extension agreed in the early hours of this morning offers a route out from the Brexit mess they have created.



“A flexible extension until 31 October is long enough to hold a people’s vote. The prime minister must now show leadership by handing the decision back to the British public.



“It is long overdue that Theresa May and Jeremy Corbyn abandon their party political games, stop wasting time, and give the people the final say with an option to stay in the EU.”