UK Prime Minister Theresa May has vowed to set a timetable for her resignation and the election of a successor at the helm of Britain’s ruling Conservative Party after pressure over the continuing Brexit impasse.

Her promise came on Thursday after she met with senior Conservative MPs demanding that she step down as party leader and Prime Minister, the BBC reported.

It cited the chairman of the 1922 Committee of Conservative MPs, Sir Graham Brady, who announced he had reached an agreement over the prime minister’s future during “very frank” talks in Parliament.

As per May’s promise, she will set her resignation timetable after the fourth parliamentary vote on her Brexit deal with the EU expected to be held by the British Parliament in early June.

The deal has been voted down three times already, and government sources are quoted as saying May would resign if it gets rejected once again.

The UK Prime Minister already survived a confidence by Conservative MPs at the end of last year. According to party rules, she cannot be challenged again until December 2019.

The Brexit impasse, however, and the Tories’ bad performance in recent local elections in England have piled pressure on her to step down as party leader and Prime Minister.

For the time being, the British MPs are expected to reject May’s Brexit deal once again, meaning that her resignation would likely come shortly, if not immediately, after that.

Meanwhile, May’s former Foreign Secretary and leading Brexiteer Boris Johnson made clear his plans to seek her post, joining a number of other Conservative Party bidders.

“Of course, I am going to go for it,” Johnson told a business conference in Manchester.

However, according to Conservative MP Phillip Lee, who favors holding a second Brexit referendum, replacing the Prime Minister would not “solve the crisis” over Brexit in the UK, nor would it build a parliamentary majority for the terms of the UK’s departure.

“Forcing the PM’s resignation and spending this summer locked in a leadership election where candidates trade ever more fantastic visions of unicorn Brexits…is neither in the interests of the Conservative Party nor of the United Kingdom,” he said.

Last month, the 1922 Committee executive narrowly decided against changing the party’s leadership rules to allow an early challenge to May.

At the same time, local associations of the Conservative Party are going to hold a non-binding vote of confidence in the Prime Minister’s leadership on June 15.

May’s cross party talks with the opposition Labor Party for finding a compromise on the Brexit deal, which seem to have reached a dead end anyway, are believed to have generated much anger among the Conservative MPs.

Labor leader Jeremy Corbyn has made it clear his party would support the Brexit deal only if it guaranteed that the UK would become part of a customs union with the EU, and would protect workers’, consumer, and environmental rights.

Liberal Democrat leader Vince Cable said his party would “happily support” the Brexit deal, provided it was subject to a “confirmatory public vote”, that is, a second Brexit referendum, a possibility that May has been ruling out.

(Banner image: Theresa May on Twitter)