The move comes as the Prime Minister battles to keep her Brexit agenda on track as she faces growing Tory tensions and reports of opposition from Brussels to a key part of withdrawal proposals.

With the shock resignation of pro-Europe transport minister Jo Johnson continuing to cause ructions in Tory ranks, Mrs May is running out of time to seal an EU exit agreement.

And in a stark warning to the PM, Tory Brexiteer Steve Baker, deputy chairman of the 80-member European Research Group (ERG) of Conservative backbenchers, and the DUP’s Brexit spokesman, Sammy Wilson, said they would oppose any agreement which they thought threatened the union and could put a trade border down the Irish Sea.

Prime Minister Theresa May is battling to keep her Brexit agenda on track. Picture: PA Wire

Time for Theresa May’s Brexit plan or general election – Brian Wilson

Writing in The Sunday Telegraph, they said: “We share the Prime Minister’s ambition for an EU free trade agreement, but not at any price, and certainly not at the price of our union.

“If the Government makes the historic mistake of prioritising placating the EU over establishing an independent and whole UK, then, regrettably, we must vote against the deal.”

Hope of getting the Cabinet to sign off on Brexit deal proposals this week appeared to be rapidly receding, as it was reported the EU had rejected London’s plans for an independent arbitration clause that could allow the UK to quit a backstop deal on the Northern Ireland border.

With both pro and anti-withdrawal Tories becoming more vocal in their opposition to Mrs May’s stance, arch-Brexiteer Jacob Rees-Mogg called on the PM to change tack.

He urged Mrs May to end the deadlock by paying the EU £20 billion to secure a “no deal plus” arrangement with the bloc after withdrawal.

Writing in the Mail on Sunday, Mr Rees-Mogg, who heads the ERG, suggested offering the financial deal to Brussels in order to “make our departure as amicable as possible”.

Previously critical of the £39 billion divorce bill the UK is set to pay the EU, Mr Rees-Mogg wrote: “It is time for convinced Brexiteers like me to compromise.

“So, at this late hour in the negotiations, we would like to make a new, generous offer to break the deadlock, to achieve a ‘No Deal Plus’.

“It would cost us money but it would finally dispel the ‘crash out’ Project Fear nightmare scenarios.”

A Government source told the Press Association: “The end part of negotiations were always going to be tough.

“There are a number of issues that need to be worked through on the Northern Ireland backstop and these are the most difficult.

“They include ensuring that, if it is ever needed, it is not permanent and there is a mechanism to ensure the UK could not be held in the arrangement indefinitely.”

Shadow Brexit secretary Sir Keir Starmer insisted Government talk of leaving the EU without a deal amounted to a political hoax.

Writing in the Sunday Times, he said: “There is no duty on MPs to surrender to a bad deal.

“To do so would be to concede to a political hoax designed to threaten rather than persuade.”

Former Cabinet minister Justine Greening, who shares Mr Johnson’s view that a fresh referendum is needed, called on Tories to oppose the PM’s Chequers proposals.

She told The Observer: “The parliamentary deadlock has been clear for some time. It’s crucial now for Parliament to vote down this plan, because it is the biggest giveaway of sovereignty in modern times.”

The view was echoed by Brexiteer Tory MP Andrew Bridgen who told a meeting of the Bruges Group: “If we can’t chuck Chequers then it’s time to chuck the Prime Minister.”

In the wake of Mr Johnson’s resignation there have been reports that other ministers are considering quitting over Brexit.

Brexiteers have insisted that the UK should not get involved with a potentially permanent backstop customs union agreement with the EU as the price of avoiding a hard border in Northern Ireland.

Theresa May warned of Commons Brexit defeat as eurosceptic Tories and DUP forge alliance