THERESA May’s fate as Prime Minister looks set to be sealed today when she meets the Tory grandee who speaks for Conservative backbenchers, as reports emerged last night that the contest to elect her successor will begin on June 10.

As the leadership crisis intensifies, May is expected to be given an ultimatum to set a firm date for her departure or face the prospect of further humiliation with a second no-confidence vote.

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Ahead of the Prime Minister’s showdown meeting with the chairman of the 1922 Committee, Sir Graham Brady, the committee’s treasurer, Sir Geoffrey Clifton-Brown, said: “I want her to give a timetable for when she will go.

“I think this blank denial from Number 10 today may be a smokescreen because she does not want to influence the outcome of the European elections. Maybe she will still quit tomorrow.”

Under existing Tory rules MPs can only bring one such motion forward a year, meaning a second vote could not take place until December.

However, executive members of the 1922 Committee of Tory backbenchers have carried out a secret ballot to change the rules, and will release the results today if May fails to set a firm exit date.

Amid growing clamour at Westminster for her to quit, it is highly unlikely senior Tory MPs would not back a second confidence vote.

Asked what would happen if the Prime Minister did not announce a resignation date, Clifton-Brown said: “I think there will be overwhelming pressure for the 22 to change the rules and hold a ballot on confidence in the Prime Minister.”

A 1922 Committee source said they expected May would stay until June 10, but warned there would be “much greater pressure” for her to go immediately if she introduces the Withdrawal Agreement Bill – which prompted Andrea Leadsom’s resignation on Wednesday.

The National: May was dealt another blow this week when Andrea Leadsom resigned as Commons leaderMay was dealt another blow this week when Andrea Leadsom resigned as Commons leader

“Hopefully what will happen is she will stand down as Tory leader I think on or before June 10, and she will hopefully remain as caretaker Prime Minister until such time as a new Tory leader is elected,” they said. “My feeling is that she will stay until June 10.”

The source said a new leader would ideally be in place by the end of the summer to get a Brexit deal through Parliament before October 31.

May has insisted she will remain as Tory leader to see her EU Withdrawal Agreement Bill voted on in the Commons and was yesterday discussing the legislation with her Cabinet.

Speculation she will today announce her exit date increased further yesterday with reports that Downing Street staff due to be off work today on a bank holiday had had their leave cancelled.

Pressure is mounting on May after Commons leader Leadsom stormed out of Government in protest at the Prime Minister’s EU withdrawal plan. Yesterday there were further demands for her to go.

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Sir David Evennett, previously viewed as a loyalist, used European election day to insist May must quit. The backbencher tweeted: “Theresa May must now resign. We need a new PM, a new Cabinet and a new approach to Brexit.”

At the Cabinet meeting, May was involved in a “frank” discussion with Home Secretary Sajid Javid, who made it clear he does not believe the Government should be “paving the way” for a second referendum.

Foreign Secretary Jeremy Hunt said he did not believe the Bill could get through the Commons, telling May it was a “step too far” to ask Tory MPs to vote for it under the current circumstances.

Earlier he said he expected May to still be Prime Minister when President Donald Trump visits the UK on June 3.

Responding to a question after a speech at the National Cyber Security Centre, he said: “Theresa May will be Prime Minister to welcome him and rightly so.”

Minister Margot James was a rare voice of loyalty, saying: “It’s all very regrettable but she’s being hounded out of office because Parliament will not make a decision and the parties just have an inability to compromise. But in the end there’s got to be a compromise.”

May yesterday appointed Mel Stride, a Remainer, as Commons leader.