May announced on Friday she was quitting over her failure to deliver Brexit, raising the prospect of a new leader who could seek a more divisive split with the EU which could lead to confrontation with the bloc or a possible parliamentary election.

British health minister Matt Hancock and former Brexit minister Dominic Raab and former House of Commons leader Andrea Leadsom on Saturday joined an increasingly crowded field to replace May.

Former foreign minister Boris Johnson, current foreign minister Jeremy Hunt, International Development Secretary Rory Stewart and former work and pensions minister Esther McVey had already announced they would stand.

About a dozen contenders in total are thought to be considering a tilt at the leadership.

The Sunday Telegraph said environment minister Michael Gove was expected to announce his candidacy on Sunday while trade minister Liam Fox and former junior Brexit minister Steve Baker did not rule out a challenge when asked on Saturday.

May failed three times to get a divorce deal she agreed with the EU through parliament because of deep, long-term divisions in the Conservative Party over Europe. It meant the original Brexit date of March 29 has been extended until October 31 to see if any compromise could be reached.

All those standing say they can succeed where she failed by building consensus or amending May's deal, although the EU has said it would not renegotiate the treaty.

"Of course we have to deliver Brexit and I will," Hancock told BBC radio.

"We have to propose a deal that will get through this parliament. We have to be brutally honest about the trade-offs."

Raab, a leading figure among pro-Brexit Conservatives, said he did not want to exit without a deal, but would do so if the EU refused to budge.

The issue is set to dominate the contest which will begin in the week of June 10 when Conservative MPs begin to whittle down the field before party members, about 160,000 according to the Sunday Telegraph, choose the winner from the final two candidates.

Surveys have suggested that the members are overwhelmingly pro-Brexit and in favour of leaving the EU without a deal.

Boris Johnson is the clear favourite with bookmakers and he has also said Britain should be prepared to exit the bloc without any deal if no acceptable agreement could be reached.

"We will leave the EU on October 31, deal or no deal," Johnson told an economic conference in Switzerland on Friday.

The party's divisions over the EU has led to the demise of its last four prime ministers - May, David Cameron, John Major and Margaret Thatcher - and there is little indication these schisms will be healed soon.

Australian Associated Press