At least 15 Conservative MPs have reportedly agreed to sign a letter of no confidence in Theresa May.

It comes after the Prime Minister told plotting Tory MPs “it’s me or Jeremy Corbyn” as she insisted a leadership challenge would trigger another general election.

Although the letter of no confidence falls short of the 48 names required to trigger a leadership contest, Parliament’s summer break could prove critical for Ms May’s future.

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A former minister told The Sunday Times: “The numbers change from day to day depending on what’s happened but there are about 15 who are fairly consistent in their desire for change.

“If she has a quiet summer and there are no crises and things are not mismanaged then she might be able to cling on beyond conference, but that is still a big if.”

At a summer party last week, Ms May pleaded with her MPs to “go away and have a proper break and come back ready for serious business”.

“No backbiting, no carping. The choice is me or Jeremy Corbyn – and no one wants him,” Conservative MPs who were present reported her saying.

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The Sunday Times’ source added: “The break will either have dissipated some of the resentment towards her for gambling away the party’s majority or the rumblings around her leadership will start to flare up again.”

David Davis topped a survey of Tory members as the candidate to replace Ms May as leader, but most wanted the Prime Minister to remain in post.

More than a fifth, 21 per cent, of Conservatives want the Brexit Secretary to take over from the ailing premier, according to a study by academics.

Foreign Secretary Boris Johnson is his main rival on 17 per cent while backbencher Jacob Rees-Mogg made a surprise entry as the third choice with 6 per cent, the party members project funded by the Economic and Social Research Council found.

But more than a quarter, 26 per cent, did not know or declined to say who they wanted to see as Ms May’s successor, according to the data obtained by The Observer.

And 71 per cent said they were reluctant for the PM to quit now compared to 22 per cent who want her to go.

Senior members of the 1922 Committee, which represents Conservative backbenchers, have indicated there is no appetite for a leadership election and that Mrs May would have their backing if she sacked plotters.