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Brexit supporter Michael Gove today backed cross-party talks on leaving the EU, calling for “the maximum possible consensus”.

The new Environment Secretary, who has rejoined the Cabinet after being sacked by Theresa May last year, did not rule out calls for a commission into the deal that the Government should seek.

Growing support among ministers for discussions with Labour sparked anger among hardline Tory eurosceptics, who fear their hopes of a hard Brexit or even no deal at all with the EU are falling away.

But Mr Gove said it was “really important” that the exit package was “in the interests of the whole country”.

Pressed on reports of secret talks between Cabinet ministers and Labour MPs, Mr Gove said the hung parliament meant that the Government would have to “work with everyone”.

He added “We need to ensure that those who voted Remain are part of the conversation about what the best deal for Britain is in the future.

“We as Conservatives were not returned with a majority and that means that we need to proceed with the maximum possible consensus and that we also need to make sure that the concerns of people who voted Remain … are part of our conversation.”

The Standard yesterday revealed that ministers opposed to a “hard Brexit” are reaching out to Labour MPs to get a Commons majority behind a softer stance towards the customs union and the single market.

Scottish Conservative leader Ruth Davidson piled on pressure for a cross-party approach, saying “we have to work with others”.

Former foreign office minister Alistair Burt, a leading Remainer, said the election result meant talks with the EU were “no longer the sole preserve of the Conservative Party”.

“It is not a matter that will be dictated between wings of the Conservative Party but it has to be, as the Prime Minister said, a national endeavour,” he said. “I agree with Ruth.”

Another senior Cabinet minister told the Standard that he believed Mrs May should open up formal discussions across the Commons.

But the minister said: “The real question is whether Labour’s front bench will allow it to happen. At the moment, they seem to have a real mood of ‘let’s bring the government down’ instead of wanting to negotiate.”

Jeremy Corbyn and John McDonnell ruled out membership of the single market on Sunday, possibly fearing that Conservatives were seeking to blame them for any backtracking from the Tory manifesto, which also ruled out single market membership.

Former Conservative leader Lord Hague wrote in the Daily Telegraph that “a change of style and substance” was needed and suggested a commission included business leaders, trade union leaders and “the leaders of all opposition parties — yes, even Corbyn”.