The Conservatives have agreed to change the rules for leadership elections to quickly eliminate candidates with little support, an MP has said.
Candidates will need to win five per cent of votes (16 Tory MPs) in the first ballot and 10 per cent (32 MPs) in the second in order to progress.
Once Conservative MPs have chosen the final two candidates, the new leader will be chosen by all members of the party, MP Michael Fabricant said in a tweet on Tuesday.
He added: "It is hoped the final two will be chosen by the end of next week and a new PM will be in place by the end of July at the latest."
The rule change had been proposed by the 1922 Committee of Tory backbenchers.
Theresa May is due to resign as leader of the Tory party on Friday, June 7, however she will remain prime minister until her successor is appointed.
The 1922 Committee is also reported to have agreed that those wanting the job would need the support of eight MPs to enter the race - a higher threshold than in previous contests.
Final candidates will be put to the party's 160,000 or so members nationwide in a postal vote which will decide Britain's next prime minister.
The rules provide the party with a way to whittle down the 11 candidates - reduced from 13 on Tuesday when two withdrew - running for the position more quickly and put an end to the uncertainty triggered by Mrs May's resignation over her failure to deliver Brexit on time.
The move comes as Kit Malthouse announced he has pulled out of the race to replace Mrs May.
He announced his decision on Twitter and gave thanks to everyone that supported him.
"I have decided to withdraw from the contest for the leadership of the Conservative Party. Thank you to all those who have supported me," he tweeted.
Mr Malthouse, MP for North West Hampshire, said he thinks there is "an appetite for this contest to be over quickly".
In a statement, the housing minister said: "When I announced my intention to seek the leadership of the Conservative Party, I did so believing that I could make a real difference in delivering a Brexit that would command the support of the House of Commons."
He then referred to his political career and "20 years in front line politics" as a councillor, deputy mayor, MP and a minister.
Mr Malthouse said that background was what made him want to lead but also influenced his decision to pull from the race.
"That experience has also made me a realist and the last few days have demonstrated that there is an appetite for this contest to be over quickly and for the nation to have a new leader in place as soon as possible.
"As such, it seems right to me that I withdraw my candidature and wish those remaining the very vest, always recognising there are going to be very challenging times ahead."
