She became the party leader after Cameron's departure and the second female prime minister of the country on July 13, 2016.
She will continue to work as prime minister until her party elects a new leader, a crowded race that will be defined by Brexit and competing approaches on how to deliver Britain's biggest policy shift in more than 40 years.
Nearly a dozen Conservative lawmakers are already jostling to replace May in a contest that formally opens Monday, vowing to succeed where she failed and renegotiate Britain's divorce deal with the European Union.
His single-issue party suffered a setback after narrowly missing out on winning its first parliamentary seat, losing to Labour in a by-election in the eastern city of Peterborough on Thursday.
The bookmakers' favourite to replace May as prime minister, tousle-haired Brexit champion Boris Johnson, has warned that the Conservatives face "extinction" if Britain doesn't leave the European Union on October 31.
It is now scheduled for October 31.
Even if the Brexit Party never gets enough votes to gain a Westminster constituency, it will split the centre-Right vote and put Labour - or at least a Labour-led coalition - in Downing Street.
Farage had clearly thought Peterborough would mark a triumphant entry for the Brexit Party into the House of Commons.
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Mr Johnson, a leading campaigner in the 2016 referendum who quit the government past year over Mrs May's plan, is among several would-be candidates who say they are willing to do this.
The letter goes on to say that there has been a "lack of activity and focus" due to the Tory leadership contest.
The Brexit Party was beaten by just 683 votes, but turnout was down almost 20 percent compared to the 2017 general election.
It all adds up to a deeply unstable situation for any new prime minister, who could also face a no-confidence vote triggered by Labour in his or her first days in office. Voters could simply choose to discount the claim if they wanted to do so, he said.
They are under pressure from euroskeptic figurehead Nigel Farage, who supports a "no deal" option and whose Brexit party topped European polls last month.
Although she had voted to remain, May insisted from day one of her tenure at Downing Street that the will of the British people must be respected.
The contest should be completed in the week commencing July 22.
Also in the running are such figures as Jeremy Hunt and Michael Gove, who say they can renegotiate the pullout agreement with the European Union to get better terms.
They will go through the usual theatre performance of saying that the United Kingdom can't have another extension, but in fact I believe that they will probably grant another one, because I just don't think that any of the candidates that are going to replace Prime Minister May potentially are really committed to a proper, clean Brexit. "I look back and I think I wish I hadn't done that", he said.