The next leader of the Conservative Party must be “somebody who believes in Brexit”, Foreign Secretary Jeremy Hunt has said, in a barely-veiled hint at his own ambitions.

At a lunch in Westminster, Mr Hunt declined to reveal whether he would stand for the leadership when Theresa May stands down, saying only: “Wait and see.”

But he made clear that he does not think his own support for Remain in the 2016 EU referendum should rule him out of the top job, insisting that he now wants “to leave, leave quickly and leave cleanly”.

Asked whether the next leader should be someone who voted for Brexit, Mr Hunt replied: “It has got to be somebody who believes in Brexit because that’s the fundamental mission of the Government at the moment.

“You have to be someone who believes – as I do and, to be honest, I think all the people who are touted as leadership contenders do – that Britain can make an extraordinary success of our post-EU future.”

Mr Hunt was speaking as pressure mounted on Mrs May to name a date to quit as Prime Minister, after an influential committee of backbenchers demanded “clarity” over what she will do if her EU withdrawal deal fails.

Mrs May has said she will step down if her Withdrawal Agreement is ratified, but – with the deadline for Brexit extended to the end of October – has not made clear how long she intends to stay if no deal is reached.

POLITICS Brexit
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The chairman of the 1922 Committee, Sir Graham Brady, said on Wednesday it would be “a surprising response” if Mrs May suggested she might stay on as late as December this year.

Mr Hunt – who once said that health secretary was likely to be his “last big job in politics” – is seen as a likely frontrunner in any race to replace her, but will face opposition from grassroots Conservatives who want the job to go to someone who campaigned for Leave in 2016, such as Boris Johnson or Michael Gove.

The Foreign Secretary said that Britain was in danger of “Brexit paralysis” and said he would opt for no deal rather than no Brexit if these were the only choices available.

“As far as Brexit is concerned, my view is very straightforward,” he said.

“We have to leave, leave quickly and leave cleanly.

“I see Brexit as the biggest democratic challenge we have had in our lifetimes. The political establishment – myself included – didn’t want Brexit or vote for Brexit, yet we’ve always been telling people we are one of the greatest and oldest democracies in the world.

“People are looking at us and saying, ‘We are going to test that, we are going to ask you guys to do something you don’t want to do, we are going to see if we really are a democracy’. It’s absolutely essential that we pass that test and then make a success of Brexit the other side.”

Mr Hunt warned there was a “very significant” risk of disruption if the Government failed to deliver on the result of the referendum by taking Britain out of the EU.

But he said he would not support an early election to try to get a majority in Parliament for a Brexit deal.

“If there was a binary choice between no deal and no Brexit, I would choose no deal, because I think the democratic risk of no Brexit ultimately is higher than the economic risk of no deal,” he said.

“But the reality is that this Parliament won’t allow no deal, and I don’t wish to go back to the country to try to get a different Parliament until we have left the EU, because that’s what we promised voters we would do at the last election and that’s what they are absolutely expecting us to do.”

The threat of an imminent challenge to Mrs May’s position as Conservative leader was lifted on Wednesday when the 1922 Committee’s executive rejected calls to change party rules which protect her from a no-confidence vote until December.

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Sir Graham Brady has called for clarity from Theresa May (Victoria Jones/PA)

But Sir Graham made clear he remained ready to convey MPs’ concerns about her leadership to Mrs May.

And he asked her to set out a “timetable and schedule” for departure if her Withdrawal Agreement fails to secure parliamentary approval.

Cross-party talks on a Brexit compromise continued on Thursday, with time growing perilously short to find a deal which could halt next month’s European elections.

The PM’s effective deputy, Cabinet Office minister David Lidington, described the talks with Labour as “productive and workmanlike”, but admitted that an eventual agreement was not certain.

“It’s not certain we’ll come to an agreement on substance but I think there is a sense of both sides that there are things we do have – important things – in common about what we want to see as an outcome,” said Mr Lidington.

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Chancellor of the Duchy of Lancaster David Lidington was speaking in the margins of the Cyber UK conference in Glasgow (Andrew Milligan/PA)

If no compromise deal can be agreed, Mr Lidington confirmed that the PM’s plan is to put a set of options to Parliament with both the Government and opposition committed to accepting the result.

“What is needed now is not just another parliamentary opinion poll where the majorities assemble against anything that’s put on the table,” he said.

“You actually need a process that means that Parliament has to endorse a third outcome, even if that for many MPs is the second or third best of what is available.”

Mrs May is running out of time to find a compromise, with most Westminster-watchers thinking she must table the Withdrawal Agreement Bill next week to have time for ratification before the May 23 Euro-elections.

But the Government is wary of moving too soon, as defeat for the Bill would force Mrs May to bring the parliamentary session to an end and schedule a new Queen’s Speech, leading to additional delay.

The Bill did not feature in the business for next week set out by Leader of the Commons Andrea Leadsom.