Theresa May told Boris Johnson she had no intention of stepping aside to help resolve the Brexit impasse at a high-stakes meeting earlier this week with the man seen as the favourite to replace her.

In the meeting, the former foreign secretary, who remains opposed to May’s Brexit deal, demanded to know how the prime minister would change approach, which was interpreted as a coded message that he believed she should quit.

May responded by saying she was drawing up plans in case her Brexit deal was carried through by the House of Commons, including a “restructuring” of the Department for Exiting the European Union, signalling she anticipated staying put.

The meeting took place in Downing Street on Tuesday, but when Johnson emerged, he was uncharacteristically silent as reporters asked questions. Since then, several informed accounts have begun circulating at Westminster.

According to one source, May even indicated she would, if necessary, be prepared to lead the Conservative party and fight a general election if one took place before 2022 – the date she has given for when she is prepared to stand down.

Tory MPs vow to quit party if Boris Johnson becomes leader Read more

Neither side offered any concessions in an effort to break the deadlock, according to more than one account, partly due to concerns that if either were to show any willingness to compromise, it would leak.

“No deal between them was done, and there was no talk of a deal,” said a person who had heard an account of the meeting. A second person said it was safe to conclude the two “weren’t in complete agreement”.

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Johnson’s opposition to May’s Brexit deal is well known and the man who hopes to become the next prime minister has made it clear he has no intention of changing his mind if May puts the plan to a vote for a third time next week.

In his Daily Telegraph column last week, Johnson said he had consulted his constituents over whether he should compromise and support May’s deal “that I believe is detrimental to the interests of this country”.

He concluded: “My constituents were strongly of the view that I should not compromise. They assured me that they would support whatever decision I took, but they believed I should continue to vote against the deal.”

Other senior Conservatives have begun telling May to her face that she should stand down. Graham Brady, the chairman of the 1922 Committee of Tory backbenchers, saw her on Monday and said a growing number of MPs believed she had to go.

Ben Bradley, the MP for Mansfield, said that he could not see how May could carry on as prime minister if her Brexit deal were voted down for a third time next week, suggesting he believed her time in Downing Street was running out.

Bradley said he was undecided whether to support May’s deal next week, despite having decided to vote for it the second time around after voting against it the first time in January.

“As it stands, and it seems that extension, delay and indicative votes are all on the table and no deal is also on the table, then I think she will lose by more,” Bradley said.

“Those people like myself who believe no deal was off the table, well, that’s obviously not the case any more. If it is the case that her deal goes backwards, I do not see how she goes on after that.”

A spokesperson for Johnson said he would not comment on private conversations.

The two Conservatives had a further meeting on Friday, as May tried again to get Johnson to support her Brexit deal, although it is not clear much progress was made on either side.

May survived a vote of no confidence in her Tory leadership in December and cannot under party rules be challenged for 12 months after that date, making it difficult for her to be ousted unless there is a widespread, open revolt against her.