LONDON (Reuters) - Fighting back tears, Theresa May said on Friday she would quit after failing to deliver Brexit, setting up a contest that will install a new British prime minister who could pursue a cleaner break with the European Union.

May’s departure deepens the Brexit crisis as a new leader, who should be in place by the end of July, is likely to want a more decisive split, raising the chances of a confrontation with the EU and potentially a snap parliamentary election.

Former foreign minister Boris Johnson, the favourite to replace May, was first out of the blocks, saying Britain should be prepared to leave the EU without a deal to force the bloc to offer a “good deal”.

Current foreign minister Jeremy Hunt also confirmed he would run for the leadership just hours after May, her voice cracking with emotion, said she would resign as Conservative Party leader on Friday, June 7, setting up a contest to succeed her.

“I will shortly leave the job that has been the honour of my life to hold,” May said outside her Downing Street official residence with her husband, Philip, looking on. “The second female prime minister, but certainly not the last.

“I do so with no ill will but with enormous and enduring gratitude to have had the opportunity to serve the country I love,” said the usually reserved May.

May, once a reluctant supporter of EU membership who won the top job in the turmoil that followed the 2016 Brexit referendum, steps down with her central pledge - to lead the United Kingdom out of the bloc and heal its divisions - unfulfilled.

“It is, and will always remain, a matter of deep regret to me that I have not been able to deliver Brexit,” May said, adding that her successor would have to find a consensus to honour the 2016 referendum result.

Jeremy Corbyn, leader of the main opposition Labour Party, said the new prime minister must hold an election to “let the people decide our country’s future”.

PM BORIS JOHNSON?

May, who endured several crises in her failed effort to find a compromise Brexit deal that parliament could ratify, bequeaths a deeply divided country and a political elite that is deadlocked over how, when or whether to leave the EU. The latest deadline for Britain’s departure is Oct. 31.

Most of the leading contenders to succeed May want a tougher divorce deal. The EU has said it will not renegotiate the Withdrawal Agreement it sealed with Britain in November.

Spain said it now seemed almost impossible to avoid a so-called hard Brexit, or clean break from the EU, and the bloc signalled there would be no change on the agreement despite European Commission President Jean-Claude Juncker learning of May’s resignation “without personal joy”.

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Irish Foreign Minister Simon Coveney underlined the bloc’s stance that there would be no better Brexit deal.

“This idea that a new prime minister will be a tougher negotiator and will put it up to the EU and get a much better deal for Britain? That’s not how the EU works,” Coveney told Ireland’s Newstalk radio station.

Politicians in her party and abroad paid tribute to her determination. French President Emmanuel Macron praised May’s “courageous work” and U.S. President Donald Trump said he felt bad for her.

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“I like her very much, she is a good woman, she worked very hard,” Trump said.

Johnson, the face of the official Brexit campaign in 2016, is the favourite to succeed May, with betting markets giving him a 40% implied probability of winning the top job..

He made his pitch at an economic conference in Switzerland, appealing to Brexit-supporting Conservative Party members by saying: “We will leave the EU on Oct. 31, deal or no deal.”

He said Britain could forge a “fantastic free trade relationship” with Europe after it quits the bloc but could also be a champion for global free trade.

Others tipped are Dominic Raab, a Brexit supporter and former Brexit secretary, with a 14% implied probability on his chances. Environment Secretary Michael Gove, former House of Commons leader Andrea Leadsom and Hunt each have a 7% probability, according to betting markets.

Defence Secretary Penny Mordaunt and International Development Secretary Rory Stewart each have a 4% chance of the top job while Home Secretary Sajid Javid has a 3% chance.

Conservative lawmaker Graham Brady resigned as chairman of the party’s 1922 Committee of backbench MPs in preparation for a potential leadership bid, the BBC said.

For many Conservative lawmakers, speed is of the essence to install a new leader to try to break the Brexit impasse.

The governing party said it would move quickly to try to end the leadership contest before parliament breaks for a summer holiday, a so-called recess which usually falls in late July.

“The fight for the heart and soul of the Conservative Party officially starts now,” said Andrew Bridgen, a pro-Brexit lawmaker. “We need a new PM as soon as possible and who that is will decide the future of our democracy, our country and the Conservative Party.”

Sterling swung back and forth on May’s resignation, and British government bond yields edged off near-two-year lows struck first thing on Friday.