All those standing say they could build a consensus or amend May's deal, although the EU has said it would not renegotiate the treaty.

"We have to propose a deal that will get through this parliament," Hancock told BBC radio. "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, a stance echoed by Leadsom, who quit the government on Wednesday over May's deal.

"To succeed in a negotiation you have to be prepared to walk away," Leadsom, who made it to the last two in the 2016 contest to replace David Cameron as prime minister following the EU referendum, told the Sunday Times newspaper.

Brexit is set to dominate the contest which will begin in the week of June 10 when Conservative lawmakers 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.