However, in Brussels, there have already been signals that the Brexit deal they negotiated with May will not be changed.
(Video reporter: Jin Jing; Video editor: Wang Han)
Bookmakers Ladbrokes on Friday listed Johnson as the favorite to win the race with odds of 5/4, the highest among other candidates.
Former Conservative party chairman Grant Shapps said the contest to replace May should be between someone who voted Remain and someone who voted Leave.
The current law on the British statute books is that Britain would leave on that date without a deal, unless a new arrangement is in place by then, which means that whoever gets the keys to Number 10 after May will also get the keys to the future of Brexit, as well as the future of the country itself.
A tearful May announced she would resign on June 7 as leader of the Conservative Party, and as prime minister who has been entasked with Brexit from the very first. May's resignation had been anticipated, but was still a dramatic moment in British politics.
The timetable agreed upon means she will still be at the forefront of those events as Britain's prime minister.
Next week sees U.S. President Donald Trump paying a state visit to Britain, and also commemorations to mark the anniversary of the World War II D-Day landings.
It would pave the way for a clash between Johnson and a Remainer in the final stage of the race.
She said she had done everything she could to convince MPs to back her deal. "It is now clear to me that it is in the best interests of the country for a new prime minister to lead that effort."
Former Foreign Secretary Boris Johnson, who also served two terms as Mayor of London and has widespread support in the shire counties among ordinary party members, is clearly the favorite to succeed May.
A new prime minister may seek to extend the October deadline to buy more time, or may even seek the revocation of Article 80, the Brussels mechanism that kick-started the process that leads to an exit from the EU.
Foreign Secretary Jeremy Hunt became the first front-line politician after May's resignation speech to throw his hat into the ring in a contest that has already thrust one of Hunt's predecessors, Boris Johnson, into the spotlight. Johnson is slated as the favorite to win by most bookmakers.
The EU has extended the date until Oct. 31 for Britain to reach an agreement on a withdrawal deal that will pave the way for its departure from the world's largest trading bloc.
In her speech May said she had done her best to implement the decision of the people of Britain to leave the European Union (EU).
May shared her speech with millions as camera crews from around the world captured her dramatic resignation announcement in front of the iconic door to 10 Downing Street.
The top two contenders will then campaign around the country as thousands of grassroots Conservative members vote for their favorite.
Her own backbench MPs had held a secret ballot to vote on whether she should effectively be shown the door. The letters were in sealed envelopes, ready to be opened Friday if she declined or refused an invitation to finally step down.
By Friday night, at least 14 contenders have emerged as a possible successor to replace May, with seven of them being senior front-bench members of May's cabinet.
In a speech on Friday in Switzerland, Johnson gave a strong hint of the Brexit outcome if he wins. "We will leave the EU on Oct. 31, deal or no deal. The way to get a good deal is to prepare for a no deal."
"It will be for my successor to seek a way forward that honors the result of the referendum," May said in her resignation speech. "To succeed, he or she will have to find consensus in Parliament where I have not."
Conservative politicians at Westminster will vote on a long list of candidates, before they whittle it down to two.
"Such a consensus can only be reached if those on all sides of the debate are willing to compromise."
May herself had been on a shortlist along with Andrea Leadsom, leader of the House of Commons who resigned this week saying she could not support May's withdrawal plan.
For now, nothing is certain except that May's successor will have to pick up the pieces in the hopes of resolving an issue that has been dividing the country.
With May's withdrawal deal dead in the water, the unfinished task will be handed to the new prime minister.
The hope is that changes in the European Parliament landscape, resulting from the current elections for Members of European Parliament, could open the door to compromise that might offer the prize May failed to win in her 1,000 or so days as prime minister.
British Prime Minister Theresa May leaves 10 Downing Street for the House of Commons in London, Britain, on March 14, 2019. (Xinhua/Han Yan)
The race that offers the keys to 10 Downing Street as the prize starts officially on June 10. But a list of likely contenders has already emerged, with some hopefuls having already stated their intentions to run.
May will remain in a caretaker role until the new prime minister takes over sometime in the late summer, depending on the length of the campaign to succeed her.
LONDON, May 25 (Xinhua) -- The search to find a new prime minister started in Britain on Friday just hours after Theresa May announced she was resigning.
Shapps speculates the contest could come down to Remain-voting Jeremy Hunt facing down either Johnson or Dominic Raab, who were both Leavers.
With May's proposal for a fourth time to bring her under-fire Brexit deal to Parliament for a vote in tatters, a deal hated as much by many of her own MPs as by those on the opposition benches, she had run out of time.