Home Secretary Theresa May is set to lead Britain from Wednesday after the ruling Conservative Party elected her to succeed Prime Minister David Cameron as party leader.

"I am honoured and humbled to have been chosen by the Conservative Party to become its leader," May said on Monday after she emerged from parliament to cheers and applause from dozens of Conservative colleagues.

She said Britain needs a "vision of a country that works for every one of us," after last month's Brexit referendum exposed social, economic and political divisions.

"Brexit means Brexit and we are going to make a success of it," said May, who had backed Cameron's Remain campaign before the referendum.

Her final rival, Vote Leave campaigner Andrea Leadsom, pulled out of the race earlier Monday.

"It's wonderful we have a serious, experienced leader in serious, dangerous times," former defence minister Liam Fox, an early challenger to May in the leadership contest, said as crowds waited for May outside parliament.

Graham Brady, chairman of the election committee, declared that May had been "elected the new leader of the Conservative Party with immediate effect," following consultations with party officials.

Cameron said he plans to meet his cabinet on Tuesday and take prime minister's questions for the last time on Wednesday before visiting Queen Elizabeth II to formally offer his resignation.

"So we'll have a new prime minister in that building behind me by Wednesday evening," he said outside 10 Downing Street, the prime minister's residence in London.

"It's clear Theresa May has the overwhelming support of the Conservative parliamentary party," Cameron said, after a large majority of the party's 330 members of parliament backed her.

"I'm also delighted that Theresa May will be the next prime minister," he said. "She is strong, she is competent, and she is more than able to provide the leadership that our country is going to need in the years ahead, and she will have my full support."

Launching her campaign earlier Monday, May, 59, said the country would remain fully committed to a Brexit under her leadership.

"There will be no attempts to remain inside the EU ... no attempts to rejoin by the back door," May told supporters and journalists.

She said a Conservative Party under her leadership would "put ourselves at the service of working people... [and] make sure our economy truly works for everyone."

Leadsom, 53, read out a letter informing the Conservatives' election committee of her decision to withdraw her candidacy.

She cited the far greater support May enjoys among Conservative lawmakers and said it was in everyone's interests to avoid a nine-week leadership campaign that would prolong the political and economic uncertainty following the June 23 referendum on Britain's exit from the European Union.

Leadsom said she believed May is "ideally placed to implement Brexit on the best possible terms."

"Business needs certainty," she said. "We now need a new prime minister in place as soon as possible."

Cameron failed to convince voters in last month's referendum on EU membership to vote against a so-called Brexit, prompting his resignation.

He was widely booed by other spectators when Wimbledon tennis champion Andy Murray mentioned the prime minister's presence following his victory in Sunday's men's final.

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