Support grew yesterday for British interior minister Theresa May's bid to succeed premier David Cameron and lead the country out of the EU, after Boris Johnson's shock withdrawal from the race.

Dozens of Conservative MPs have backed her bid to take over from Cameron, who announced his resignation after losing a referendum last week in which 52 percent of Britons voted to quit the EU.

Britain has been plunged into extraordinary political turmoil since the Brexit vote, with the ruling Conservatives and opposition Labour party in disarray and the country deeply polarised.

May supported the "Remain" campaign but has assured "Leave" supporters she will proceed with Brexit although she said she would not begin formal talks with the EU before the end of the year.

The Daily Mail newspaper, widely read among Conservative grassroots who will ultimately select the new leader, endorsed her with a front-page headline saying: "A party in flames and why it must be Theresa".

Justice minister Michael Gove, a top Brexit campaigner who torpedoed former London mayor Johnson's chances by announcing his own candidacy on Thursday, is seen as May's main rival.

"This country voted for change and I am going to deliver it," he said in a speech in which he repeatedly stressed May's support for "Remain".

"The best person to lead Britain out of the European Union is someone who argued to get Britain out of the European Union," he said, adding that he would clamp down on immigration if he becomes leader.

"I will end free movement (of EU nationals), introduce an Australian-style points-based system for immigration, and bring numbers down," he said.

Cameron, who promised the referendum in what was seen as an effort to see off a challenge from the anti-EU UK Independence Party (UKIP), has said he will leave it to his successor to start formal exit talks.