Even after surviving a no-confidence vote last December, British Prime Minister Theresa May will set a timetable for her exit from Downing Street early next month, kicking off the race for leadership between the possible replacement candidates.

The agreement follows a meeting between the prime minister and senior Tory MPs who are demanding a date for her departure from Downing Street. May has come under increasing pressure to leave Downing Street this summer, amid the Brexit impasse and poor results for the Conservatives in the recent local elections in England.

BBC political editor Laura Kuenssberg said senior sources had told her it was "inconceivable" the prime minister could remain in office if MPs rejected her Brexit plans for a fourth time.

Sir Graham Brady, chairman of the 1922 Committee of Conservative MPs, said he will meet May to agree on the details of her exit from Downing Street and discuss her future following the first debate and vote on the Withdrawal Agreement Bill in the week beginning 3 June. Brady added there was now "greater clarity" about the situation. 

Former foreign secretary Boris Johnson has joined the growing list of Conservatives who say they will stand for leader when May announces her departure.

Downing Street said the statement had been issued with the consent of the PM.

"The PM's focus is on securing our departure from the EU and we are working incredibly hard to build a stable majority for the WAB ahead of its introduction," May’s spokeswoman said.

Earlier this year, May promised to resign once her Brexit deal had been passed by parliament. The House of Commons has rejected the PM's deal three times, forcing May to delay Brexit twice.