Michael Gove has thrown beleaguered Theresa May a lifeline after deciding that he will remain in her Government as Environment Secretary.

Following the resignation of four ministers in the wake of her poorly-received Brexit deal on Thursday, speculation was rife that the departure of the most senior Leave campaigner in her Cabinet could deal a damaging blow to the Prime Minister.

But a source close to Mr Gove told the Press Association: “Michael is staying at Defra (the Department for Environment, Food and Rural Affairs).

“He thinks it is important to continue working with Cabinet colleagues to ensure the best outcome for the country.”

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Environment Secretary Michael Gove was tight-lipped as he arrived for work in Westminster (Victoria Jones/PA)

Asked whether she could afford the loss of Mr Gove from her team, Mrs May told LBC: “I want all of my colleagues in the Cabinet to feel able to carry on doing the excellent job they are doing.”

Mr Gove was reported to have been offered the post of Brexit Secretary vacated by Dominic Raab, but to have said he would only take it if he could renegotiate the EU withdrawal agreement.

Mrs May said she had “a very good conversation” with Mr Gove on Thursday, but declined to say what they had discussed, other than the future of the fishing industry after Brexit.

She said the Environment Secretary had been doing “a great job”, adding: “I haven’t appointed a new Brexit Secretary yet, but obviously I will be doing that over the course of the next day or so.”

In a half-hour phone-in on the radio station, Mrs May faced repeated calls to stand down from members of the public.

One caller told the PM that Jacob Rees-Mogg would make a better leader, while another said she had “appeased” the EU like Neville Chamberlain in his negotiations with Hitler.

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Theresa May defended her Brexit plans in a Downing Street press conference on Thursday (Matt Dunham/PA)

Meanwhile, former Cabinet minister John Whittingdale confirmed he has submitted a letter of no confidence in Mrs May as Conservative leader.

His letter brings to 18 the tally of MPs publicly declaring they have written to Sir Graham Brady, the chair of the backbench 1922 Committee, with Westminster insiders believing the total may be near the 48 needed to trigger a vote.

A senior Brexiteer source said the number was “close” to 48, adding: “People are consulting with their associations over the weekend.”

Mr Whittingdale told the Press Association: “I believe that the agreement that is being proposed does not deliver Brexit in the way that I and many others want to see.”

Former defence minister Mark Francois, the vice-chair of the European Research Group of Eurosceptic Tories, published his own letter, denouncing the Brexit deal as “truly awful” and warning: “I can never vote for this and neither can many of my colleagues.”

Mrs May played down suggestions that she might seek to maintain Cabinet unity by offering ministers a free vote when the Brexit deal comes before Parliament.

“There is Cabinet collective responsibility in this country. Government policy is Government policy,” she told LBC. “The Government will put its position to the House of Commons.”

The PM denied that she had had a “testy exchange” over Brexit with Arlene Foster, the leader of the Democratic Unionist Party, which props up her minority administration in the Commons.

But she left no doubt she was aware she cannot guarantee DUP support when Brexit comes to the Commons, saying: “Every individual MP will decide how they will vote, whether they are DUP, Conservative, Labour.

“My job is to persuade first and foremost my Conservative benches, those who are working with us – the DUP are working with us, obviously, confidence and supply – but I want to be able to say to every MP I believe this is the best deal for the UK.”

Mrs May was forced to defend her deal with Brussels to a series of callers, including Conservative-supporting councillor Daniel Turner from Louth who told her to “stand down and allow someone from the Brexit camp to take the lead”.

Asked whether she saw herself as a “modern-day Chamberlain”, she replied: “No I don’t … What we are doing is negotiating a deal that means we can take back control of our borders, free movement will end once and for all. We take back control of our money, we won’t be sending vast sums of money to the EU every year.

“We take back control of our laws, we won’t be under the jurisdiction of the European Court of Justice. We come out of some of the things that people have been really concerned about for years – Common Agricultural Policy, Common Fisheries Policy. We’re out of the customs union, out of the single market.

“I think that’s what people voted for and that’s what I’m delivering.”

Former Brexit Secretary David Davis denounced the draft deal agreed by Cabinet on Wednesday as a “dreadful proposal” and suggested it was still possible to reopen negotiations with Brussels.

“The European Union has spun this out deliberately to try to use time against us,” he told the BBC Radio 4 Today programme. “But European negotiations are never over until they are concluded.”

His comment earned a stinging rebuke from former Foreign Office permanent secretary Sir Simon Fraser, who said: “David Davis was a terrible Brexit secretary. He could hardly be bothered to go to Brussels and rapidly lost respect there.

“Preposterous for him now to suggest that EU deliberately delayed negotiations. They spent months waiting for him to engage.”

Shadow chancellor John McDonnell claimed Labour could secure a Commons majority for a “compromise” Brexit deal.

Mr McDonnell said a “unity platform” was emerging at Westminster to avoid the “catastrophic” impact of a no-deal break with the EU.

“I think we can secure a majority,” he told the BBC Radio 4 Today programme.

“People have looked over the edge of a no-deal Brexit and realised it could be catastrophic for our economy.

“Our European partners, I think, also have looked over the edge of a no-deal Brexit and seen what an impact it could have on their economies.

“So I think what is emerging within the House of Commons now is almost a unity platform to avoid a no-deal.”