And the pack will be whittled down to just two candidates on Thursday.
Party members will then decide the new leader – and the country’s new prime minister.
Here are the MPs left vying for the leadership and where they propose to take the country.
– Boris Johnson
The former foreign secretary remains the clear front-runner, having dominated all the rounds of voting so far.
Mr Johnson, a leading figure in the Leave campaign, says Britain must leave the EU by October 31, regardless of whether a fresh deal has been brokered with Brussels.
He has insisted he does not want Britain to depart without a deal, but that the Government must prepare for that eventuality as a “last resort”.
Mr Johnson was educated at Eton before arriving at Oxford University, where he would associate in the Bullingdon dining club with former PM David Cameron.
A journalist by profession, he was first elected to Parliament in 2001 while editor of The Spectator magazine.
He would hold two posts as a shadow minister – once under Mr Cameron – before leaving Westminster to take the helm at City Hall for two terms as mayor of London.
It was that job he chose to focus on when he launched his bid for the Tory crown, and not his two-year stint as foreign secretary which came to an end last year.
Joining his opponents in a TV debate for the first time on Tuesday, Mr Johnson said he would lift the National Insurance threshold for the low-paid, but added that there should be a “debate” about the 40p higher income tax rate, which currently kicks in at £50,000.
Addressing the October 31 deadline for Brexit, he said it must be met “otherwise, I’m afraid, we face a catastrophic loss of confidence in politics”.
Mr Johnson soared past his colleagues in the third round of voting on Wednesday with 143 votes, 89 votes ahead of his nearest rival.
– Sajid Javid
Born in Rochdale to Pakistani Muslim immigrants and educated at a state school, Mr Javid went on to study at Exeter University before entering finance and then politics.
His rise saw him hold several Cabinet posts, including his current role as Home Secretary.
Mr Javid’s leadership pitch sees him pledge to change the image of the Tories across the country, while stressing his comparatively humble beginnings as the son of a bus driver.
He said it was time to follow the Scottish Tories and “leave the short-term comfort zone and throw out central casting” by picking a fresh face.
On Brexit, Mr Javid said the UK must prepare for no deal, but insisted he could get an agreement through Parliament by October 31.
In Tuesday’s TV debate, he said it had been a “mistake” to have a flexible deadline, and the October 31 date would concentrate minds on both sides of the Brexit negotiations.
He narrowly survived the third round of voting with 38 votes.
– Michael Gove
Another leader of the Vote Leave campaign, Mr Gove calls Brexit an “unashamedly personal” matter for him.
But he has taken a more temperate approach than others, saying he would be prepared to delay the severance beyond October if negotiations were making good progress.
Born in Edinburgh, he was adopted and educated at a state school before winning a scholarship to the private Robert Gordon’s College and a place at Oxford University.
Mr Gove entered Westminster in 2005 and held the top jobs at the education and justice departments, before taking his current post as Environment Secretary.
Despite the lengthy career in high office, his leadership bid was rocked when he was forced to admit he took cocaine around 20 years ago when he was a journalist.
He tried to get his campaign back on track, taunting his rival and sometimes enemy Mr Johnson for pulling out of his last leadership bid.
He highlighted during Tuesday’s TV debate that the Withdrawal Agreement had already been rejected three times, and said “you cannot simply re-present the same cold porridge for a fourth time and ask people to say that’s what they want”.
Mr Gove was far behind “frenemy” Mr Johnson in the third round of MPs’ voting, but put on 10 votes from the second round to reach 51.
– Jeremy Hunt
The son of Admiral Sir Nicholas Hunt, he was educated at the prestigious Charterhouse school before attending Oxford as a contemporary of Mr Johnson and Mr Cameron.
He made his wealth after setting up an educational publishing firm, and entered Parliament in the same year as Mr Gove.
Mr Hunt has been installed as a secretary of state four times and currently heads the Foreign Office.
Pitching for Tory leader, he stated his case as a “serious leader” for a “serious moment” in the nation’s history.
He warned his party colleagues that the Conservatives would be “annihilated” if they entered a general election before Brexit.
During Tuesday’s debate, Mr Hunt said he would delay beyond October 31 if a deal was in reach, as “if we were nearly there, then I would take a bit longer”.
Mr Hunt secured 54 votes in the third round of voting, putting him in distant second place behind Mr Johnson.