THERESA May is at war with her own party after refusing to accept Brexiteer demands to name the date for her resignation.

In a meeting with Graham Brady, the chairman of the influential 1922 committee of Tory backbenchers, she resisted his plea to set out a clear timetable.

Instead, the Prime Minister promised to put her Brexit deal back to the Commons for another meaningful vote before European elections on May 23.

She also said she will discuss her future with the 1922 committee’s executive next week.

The Prime Minister has promised to quit as Tory leader when the first phase of Brexit negotiations is finished.

Some in the party believe that means May could try to stay in No 10 until the annual party conference in the autumn.

A Downing Street source said: “The PM made a very generous and bold offer to the 1922 Committee a few weeks ago that she would see through phase one of the Brexit process and she would leave and open up for new leadership for phase two.

“That’s the timetable she is working towards. She wants to get Brexit done.”

Frustration among Tories is reaching boiling point.

Party chairmen have called an extraordinary general meeting next month to hold a vote of no confidence in May’s leadership.

During Prime Minister’s Questions on yesterday, one of May’s own MPs urged her to stand down.

Andrea Jenkyns said May had “tried her best” but had “failed”.

The Tory MP told the Commons: “She has failed to deliver on her promises. We have lost 1300 hard-working councillors, and sadly the public no longer trusts her to run the Brexit negotiations.

“Is it not time to step aside and let someone new lead our party, our country and the negotiations?”

May said this was “not an issue about me”.

“If it were an issue about me and how I vote, we would already have left the European Union,” she added.

Another Leave-supporting Tory MP said she will not campaign and might not even vote for her party’s candidate in European elections.

Asked during a radio interview if she would be voting, Maria Caulfield said: “I don’t know, I’m not going to say. I may not vote at all. I fundamentally disagree with holding these elections.”

The MP said she would not vote Ukip, but pressed on whether she might back Nigel Farage’s Brexit Party, she said: “I don’t know. I will wait and see what the candidates are and make my decision then.”

Former chancellor George Osborne described May as a “lame duck”.

Osborne said his old party needed to “confront the truth, which is that it needs a new leader, it needs a new agenda, it needs to win over supporters who have disappeared from it and it needs to make an appeal to the urban, metropolitan Britain that has currently turned its back on conservatism.

“If that continues to be the trend, then there won’t be a Conservative government for much longer.

“There is a point where you have to ask yourself how many more elections are we going to lose?

“We lost the majority in 2017, we got hammered in the local elections earlier this month and now we have got the European elections where it is possible that for the first time in its long and distinguished history the Conservative Party is going to come fourth in a national poll.”

Meanwhile, Andrea Leadsom said she is “seriously considering” standing for the leadership.