Who are the MPs likely to challenge Theresa May?
But who are likely to be the runners and riders?
Prominent Brexiteer and former Foreign Secretary Boris Johnson (joint favourite at 5-1 with Ladbrokes) is a leading voice of opposition to Mrs May's Brexit plan.
The colourful Old Etonian was one of the key players in the 2017 Leave campaign and resigned from the cabinet following the Chequers summit in July.
He was heavily tipped as a successor to David Cameron but ruled himself out of the 2016 leadership contest after Michael Gove made a last-minute bid for the top job.
In a diary piece for the Spectator, Mr Johnson compared his former "late night binges of chorizo and cheese" and recent weight loss to Brexit: "We know that we have to make certain changes if we are to leave the EU."
Mr Johnson refused to rule out challenging Theresa May for her premiership in at interview at the weekend, saying the British people should not "underestimate the deep sense of personal responsibility I feel for Brexit'".
Mr Johnson, 54, who was Mayor of London for eight years, recently announced his divorce from his wife Marina Wheeler, a human rights lawyer.
Former Brexit Secretary Dominic Raab (joint favourite with Boris Johnson at 5-1 with Ladbrokes) has refused to rule out standing in a leadership contest.
Mr Raab, a prominent Brexiteer in the referendum campaign, was appointed as Brexit Secretary in July but resigned from the role in November, saying he could not support Mrs May's deal.
In his resignation letter to Theresa May on November 15, he wrote: "I understand why you have chosen to pursue the deal with the EU on the terms proposed, and I respect the different views held in good faith by all of our colleagues."
Mr Raab, 44, has been the MP for Esher and Walton since he was elected in 2010. The son of a Czech-born Jewish father who came to Britain in 1938, he is married with two children.
In his interview with the Spectator, Sajid Javid signalled his leadership ambitions by arguing that he wanted the Tories to be the party of social mobility.
On Wednesday he said he was backing Theresa May in the contest but he could still throw his hat in the ring if she loses the first vote.
The odds on Javid taking the top job are currently 8/1, according to Ladbrokes. He didn't stand in the 2016 leadership race but has since emerged as one of the favourites in Westminster to succeed Mrs May.
Javid, 49, who backed Remain in the referendum but has since positioned himself as a firm Leaver, became the first home secretary from an ethnic minority background when he was appointed in April 2018.
The son of a Pakistani bus driver from Rochdale, he was managing director at Deutsche Bank before becoming an MP in 2010. He is married with four children.
Michael Gove (third at 7-1 with Ladbrokes) appeared to rule himself out of the running in recent days.
With other senior members of the Cabinet reportedly manoeuvring to replace Mrs May if she had lost Tuesday's ultimately postponed Commons Brexit vote, Mr Gove said it was "extremely unlikely" that he would stand as a future Conservative Party leader.
That apparent reluctance could have something to do with his previous bruising experience in a Tory leadership race.
In June 2016, Mr Gove, who was campaign manager for Boris Johnson's failed drive to succeed David Cameron, withdrew his support on the morning that Mr Johnson was due to declare and threw his own hat in the ring instead.
He came third in the first round of voting, trailing behind ultimate winner Theresa May and Andrea Leadsom.
Mr Gove, 51, was born in Edinburgh, studied English at Oxford and was a journalist before becoming an MP. He is married to Daily Mail columnist Sarah Vine.