Following a series of ballots among Conservative MPs and party members, the identity of the new premier is expected to be announced on September 9.
Here are the five contenders.
May is seen as an effective, hard-working operator who has been interior minister, one of the government’s hardest jobs, for six years under Cameron.
While the 59-year-old backed the “Remain” campaign in the referendum, she is not seen as a passionate supporter of the EU.
She takes over as likely frontrunner after former London mayor and Leave campaign figurehead Boris Johnson sensationally announced Thursday he would not stand in the race after all.
She said she would steer Britain through “political and economic uncertainty” and ruled out an early general election before 2020 or a second referendum.
May also said she would not invoke Article 50 — the procedure for leaving the EU — this year, despite pressure from EU leaders for Britain to hurry up.
The bespectacled 48-year-old justice minister is seen as an intellectual leading light of the Conservative Party.
He revealed himself to be an effective campaigner for the “Leave” camp in the referendum although he is seen as lacking a popular touch with grassroots supporters.
He announced his surprise decision to run with an attack on Johnson, saying the colourful politician “cannot provide the leadership or build the team for the task ahead”.
His decision to oppose Cameron in the EU vote was hugely personal — the two have been friends and political allies for years and Gove was the godfather to the prime minister’s late son Ivan.
The work and pensions minister is relatively low-key but his working class roots make him an attractive candidate to some in a party often perceived as elitist and distant from ordinary voters.
Raised on a council estate by a single mother, 43-year-old Crabb is a committed Christian who is seen as amiable and conscientious but a long shot for the leadership.
He backed EU membership and is running on a dual ticket with business minister Sajid Javid, the son of a Pakistani bus driver, who would likely be named finance minister if Crabb became premier.
The right-wing, anti-EU Fox is a former defence minister who resigned in 2011 amid questions about his links to a lobbyist friend.
Fox, a 54-year-old former family doctor, stood unsuccessfully against Cameron in the last Conservative leadership election in 2005 and is seen as having only an outside chance this time.
He does, though, have strong support among some sections of the Conservative party membership.
A former banker and fund manager, Leadsom was one of the leaders of the “Leave” campaign.
The 53-year-old was first elected to parliament in 2010 and served in the finance ministry.
She was made a junior minister in the energy and climate change department in May 2015.
Announcing her candidacy on Twitter on Thursday with the hashtag #FreshStart, she wrote: “Let’s make the most of the Brexit opportunities!”