Health Secretary Matt Hancock released a Brexit strategy that allows for a further delay to the UK’s exit date, joining Michael Gove and Rory Stewart in effectively ruling out no-deal.

Home Secretary Sajid Javid also refused to rule out extending Britain’s departure from the EU beyond the end of October, although he claimed he “cannot envisage the circumstances” where he would do so.

But Andrea Leadsom, the former leader of the House of Commons whose resignation brought down Theresa May, insisted that what she called a “managed exit” without a deal can be delivered.

Matt Hancock released a Brexit strategy that allows for a further delay to the UKs exit date

It came as a 13th candidate entered the race to lead the Conservatives and become Prime Minister, with the former minister Sam Gyimah joined the field as the only candidate to support a second EU referendum.

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Former Tory grandee Ann Widdecombe, who quit the party and was elected as an MEP for the Brexit Party, said the number of candidates showed the Conservatives had “gone mad”.

Unveiling his Brexit plan, Mr Hancock said that the “real choice is between leaving with a deal and no Brexit,” adding that “no-deal Brexit is not a policy choice available to the next Prime Minister”.

Sajid Javid has refused to rule out another Brexit extension

Pledging to be “honest about the trade offs as we leave the EU”, he said it was impossible to have complete control over the UK’s laws while maintaining frictionless access to trade.

Mr Hancock said that as Prime Minister, he would “immediately” enshrine the rights of EU citizens living in the UK in law, and set up an “Irish Border Council” to resolve the most difficult issue in Brexit talks.

Modelled on multiparty negotiations to secure the peace process, the council would also include representatives from the Republic of Ireland and the EU to develop a solution to the border issue that is acceptable to all sides.

However, he also said he would seek a time-limit to the border backstop element of the UK’s Brexit deal, something that the EU has repeatedly rejected.

Meanwhile, appearing on the BBC’s Andrew Marr Show, Mr Javid said the Irish border was “the tail that wags the dog” on Brexit and said new technology could avoid the need for the backstop, which would keep the UK under EU trading rules if no solution for the border is found.

“We need to make sure we can do more to build that goodwill in Ireland and build their confidence,” the Home Secretary said.”What I would do is make a grand gesture to Ireland that we would cover all their costs - the upfront costs, the running costs - of a new digitised border.

“I think it could be done in a couple of years, but I think we could cover their costs.”

Mr Javid was asked whether he would ask to delay Brexit beyond the end of October, and said: “I’m clear that my plan would be to leave on October 31. I want to leave with a deal but if I have to choose between no-deal and no Brexit I would pick no deal.”

But pressed again, he added: “That’s not something I would do, but we are a parliamentary democracy and what we’ve seen in the last few months is Parliament has taken on some extraordinary powers to initiate its own legislation so if it’s statute, if it’s the law, I would not break the law if I was prime minister, of course I would observe the law.”

In her own interview on the Andrew Marr Show, Ms Leadsom unveiled a “three-step plan for a managed exit” which she insisted was not the same as leaving without a deal.

“I think it’s based on the premise that, number one, we have to leave the EU at the end of October, and, number two, the Withdrawal Agreement Bill is dead - the EU won’t reopen the Withdrawal Agreement and the UK Parliament won’t vote for it,” she said.

Meanwhile, in a series of posts on social media, Mr Stewart said no-deal Brexit was a “recipe for further delay and uncertainty” that would undermine the UK’s “300 years of reputation for economic competence”.

The International Development Secretary received a significant endorsement from within the Cabinet as David Gauke, the Justice Secretary, said Mr Stewart’s unconventional style had “real strengths” and could win an election.

Mr Gauke also said he would not be able to serve in a cabinet which pursued leaving without a deal as its “objective”.

“I don’t think you can completely take it off the table because the European Union might refuse any kind of extension and we might find ourselves in that situation,” Mr Gauke said.

“So I accept that we should prepare for it but if it is an objective in saying ‘no-deal is the right answer’ I wouldn’t support that policy, I wouldn’t be able to serve in a cabinet that pursued that policy.”

Mr Stewart also won support the former Chancellor and Father of the House, veteran pro-EU Tory Kenneth Clarke, while former Cabinet minister Nicky Morgan said she would back Mr Gove.

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