Theresa May has signalled she may be willing to compromise further with the EU on her under-fire Chequers proposals for Brexit, risking anger from Tory eurosceptics.

The prime minister used an interview at the opening of Conservative conference to urge Brussels to set out detailed concerns and bring forward counter proposals, referring to her own plans as the only ones available “at the moment”.

The move risks further antagonising those in her party who want her Chequers plans dropped altogether, with both Boris Johnson and David Davis branding them unworkable on Sunday.

The prime minister did receive some support however, including from Scottish Tory leader Ruth Davidson, who called for the party to back her and launched a scathing attack on Mr Johnson.

It comes at the start of the Tories’ annual event in Birmingham where attempts to refocus the party on the domestic agenda look set to be overshadowed by Brexit squabbling.

Once the conference is finished there will be just two weeks until the next European Council summit at which Ms May had hoped to have a Brexit deal wrapped up.

But with leaders having said her proposals “will not work” as they stand, she sought to send them a message, saying: “They’ve said they have some concerns with the proposals we’ve put together, let’s hear what those detailed concerns are.

“If they have got counter proposals, let’s hear what those counter proposals are.”

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She added on the BBC’s Andrew Marr show: “Chequers, at the moment, is the only plan on the table that delivers on the Brexit vote in the way I’ve set out.”

The prime minister did also seek to reassure eurosceptics in her party, saying “I do believe in Brexit” following questions raised about her commitment to withdrawal.

They’ve said they have some concerns with the proposals we’ve put together, let’s hear what those detailed concerns are Prime minister Theresa May

On Saturday The Independent revealed officials have already started working on an evolved ‘Chequers 2’ proposal, with some adjustments that the prime minister hopes will make it more amenable to the European Union.

Meanwhile, some cabinet ministers are still hoping to push the prime minister towards a Canada-style free trade deal, an approach Ms May had rejected.

Among those in the wider party who spoke out against her plans on Sunday morning were former Brexit secretary Mr Davis, who resigned over the PM’s approach.

He said: “It’s just wrong. It doesn’t do either what the referendum led people to expect, bringing back control of laws, in fact it explicitly doesn’t do that.

“It doesn’t bring back control of borders, so those two things straight away – there’s much more than that.”

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The former cabinet minister distanced himself from Mr Johnson however, who had in the morning papers appeared to attack the PM, as well as her proposals.

Mr Davis said that regardless of his criticism of her approach, he would still back Ms May in any vote of confidence and criticized Mr Johnson for conflating leadership and policy issues.

Asked if Mr Johnson would make a good leader, Mr Davis said: “You take what he said this morning in the papers – he talks about cancelling HS2 and spending it on a bridge to Northern Ireland.

“Well, I don’t want to do that, I think one of the blights of British politics is politicians having fantastic ideas, that cost a fortune and don’t do much good, and that would be one of them.”

Ms Davidson called the language that Mr Johnson had used in his attacks on her plans unwise.

She also questioned Mr Johnson’s claims that he only backed Ms May’s plans while foreign secretary last December, because the prime minister misled him over critical elements.

Ms Davidson said: “This is someone who was praising what the prime minister had brought home in terms of moving on to the next stage last December, someone who was in one of the great offices of state, who was sitting round the cabinet table, who now says that he was in some way deceived.

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PRESS ASSOCIATION Photo. Picture date: Saturday June 23, 2018. See PA story POLITICS Brexit. Photo credit should read: John Stillwell/PA Wire John Stillwell PA People's Vote march – demanding vote on final Brexit deal Crowds gather on Pall Mall PA People's Vote march – demanding vote on final Brexit deal A man resembling Britain's Foreign Secretary Boris Johnson, joins EU supporters Reuters People's Vote march – demanding vote on final Brexit deal EU supporters, calling on the government to give Britons a vote on the final Brexit deal, participate in the 'People's Vote' march in central London, Britain June 23, 2018. 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“I don’t sit around the cabinet table I’m not in government…but I knew what was being said in December, I’m not sure how the former foreign secretary didn’t.”

Ms Davidson called the PM’s proposals “credible”, adding: “There is a deal to be done and I support the prime minister in getting it.