A new prime minister will be in Downing Street by July 22 after the Tories agreed a leadership rule change to speed up the race to replace Theresa May.
The party has agreed proposals requiring any MP who wants to stand to be backed by eight other colleagues.
Under the previous rules, all the candidates would have needed only two MPs supporting them.
Eleven MPs are still in the race and the deadline for contenders to put their names forward closes on June 10.
Front-runner Boris Johnson was dealt a blow yesterday after leading Tory pollster Lord Robert Hayward suggested the former foreign secretary was too divisive to lead the Conservative Party to general election victory.
At a Westminster briefing, Lord Hayward described the Tory leadership favourite as a “classic Marmite” politician.
He said that while Mr Johnson attracted Brexiteer votes the Tories would not get elected under him if he did not pick up swing voters who were more concerned about competence in Government.
He told reporters: “Boris Johnson is pitching to MPs at the moment saying ‘I’m the one who can win’. I’m saying there is another substantial part to that message. That is that you can’t stop at Brexit and win an election.
“You need Brexit voters as Tories but above and beyond that you need swing voters that are not going to be put off and Boris doesn’t have that yet.”