Boris Johnson, the former foreign secretary and front-runner to succeed May, highlighted the possibility on Friday, telling an economics conference in Switzerland that his country would "leave the European Union on October 31, deal or no deal".
"The person who will replace her will embrace the possibility of a no deal with alacrity rather than fear", said Steven Fielding, professor of political history at the University of Nottingham. I've got very important experience in that respect. "We will leave the European Union on October 31, deal or no deal, former foreign minister Boris Johnson said in Switzerland".
Mr Raab said in the Mail on Sunday that the country needed to demonstrate "unflinching resolve to leave", with or without a deal. She withdrew after a backlash to an interview in which she said being a mother gave her more of a stake in the future of the country than her rival Theresa May.
"The second female prime minister - but certainly not the last", May said. "It's time for a new direction".
The EU has said it will not renegotiate the Withdrawal Agreement it sealed with Britain in November.
Gove, now environment secretary in the United Kingdom, has told MPs that he is a "unity" candidate with the "vision" and proven "grip" over government departments that will enable him to secure the UK's departure from the United Kingdom and reverse the Tory decline in the polls.
Sparks began to fly in the contest with Mr Stewart saying he would refuse to serve in a government lead by Mr Johnson as he appeared to compare the ex-foreign secretary to Pinocchio.
The Brexit process has also confirmed a rightwards drift in the ruling party, something Bale thinks could accelerate under Johnson and Raab.
Hot favourite Boris Johnson claims he is a proven victor who can see off both Jeremy Corbyn and Nigel Farage at a stroke.
In what is likely to be seen by many as a dig at Mr Johnson, the International Development Secretary tweeted: "The star name will not always be the best choice".
Treasurer of the highly influential 1922 Committee of backbench Tory MPs Sir Geoffrey Clifton-Brown expressed surprise at Mr Stewart's stance on not serving under Mr Johnson. 'I think it would be a huge mistake.
Asked if he thought the contest was Mr Johnson's to lose, the Tory grandee said: "No". For me, Boris is the only one who fits the bill.
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UK Health Secretary Matt Hancock, 40, becomes the latest Cabinet Minister on Saturday to declare his intentions to stand for the Conservative leadership after May's resignation.
But other candidates have stressed the need to get a Brexit deal through Parliament.
"The prime minister tried her best, but it is impossible to ignore the sense of drift in recent months. She has made the right decision - and I hope that the spirit of compromise is continued".
She told the Sunday Telegraph that she would back a contender who supported Leave in the 2016 referendum.
"Faced with (a no deal) situation, I think there may well be a majority in the House of Commons willing to bring about some form of public vote and that could include a general election", Labour finance spokesman John McDonnell told BBC radio.
"He has now come out and said yesterday that he is going for something which I believe is undeliverable, unnecessary and is going to damage our country and economy".
Phinnemore said there is "very little indication" that any of May's potential successors have a credible plan to take Brexit forward.
International Trade Secretary Liam Fox refused to rule himself out as a candidate.
"This isn't a matter of asking people to be disloyal to their beliefs or their party", he told the BBC.
Boris Johnson or whoever replaces Theresa May in 10 Downing Street will face the same problems and fear the same outcome, which could make a no-deal Brexit seem like a risk worth taking. Those on her own benches who fought so hard for her departure may soon come to realise the truth of the old adage, be careful what you wish for.