Former Tory Party leader William Hague has issued a blunt warning to Cabinet Brexiteers not to push their demands for a clean break with the European Union too far.
Ahead of crunch Cabinet talks at Chequers on Friday, Lord Hague said Parliament could force a "watered-down" Brexit on the Government if ministers fail to agree a compromise plan on Britain's future customs relationship with the EU.
Writing in The Daily Telegraph, he said that any minister who chose that moment to quit would show they were not fit to hold high office in the first place.
Amid reports of ministers preparing possible leadership challenges, he warned that the "vast sensible middle" of the Conservative Party "deeply dislike naked manoeuvring to become the next leader".
He said: "Flouncing out, just when the going gets tough but when the EU Withdrawal Act has been successfully enacted, will look like evading responsibility for choices that were inevitable just when important progress has been made."
His intervention will be seen as a shot across the bows to senior ministers, such as Foreign Secretary Boris Johnson, who have reportedly been considering resigning if Theresa May gives too much ground to those pressing to keep Britain as close to the EU as possible after Brexit, potentially triggering a leadership contest.
On Monday, Mr Johnson risked further inflaming tensions within the party when he publicly defended backbencher Jacob Rees-Mogg after he warned the Prime Minister she faced the collapse of her government if she failed to deliver on her Brexit promises.
The intervention by Mr Rees-Mogg, the leader of the pro-Brexit European Research Group of Tory MPs, sparked a furious backlash, with Foreign Office Minister Sir Alan Duncan accusing him of "insolence" in threatening Mrs May.
However Mr Johnson insisted that Mr Rees-Mogg was "a principled and dedicated MP who wants the best for our country".
In his article, Lord Hague warned that the Brexiteers did not have the numbers in Parliament to force through their vision on a "hard Brexit" and urged them to think through the consequences of creating a leadership crisis.
"Everyone threatening Theresa May with chaos, revolt, resignations, and a leadership election if she doesn't do as they wish needs to think carefully about what might be the consequences of their actions," he said
"A vote of no confidence in the leadership called on this issue would in all probability rally the sensible middle to the Prime Minister.
"If ardent Brexiteers push too hard, they will end up without their main objective. If there is no agreement this week on a plan for customs arrangements, the Commons will be much more likely to vote in the near future to stay in the customs union in its entirety.
"The choice is either to back a compromise plan now or to end up with a more watered-down version of Brexit that would be forced on ministers anyway."
In a further rebuke to Mr Johnson - who reportedly said "F*** business" when some firms began expressing worries about the progress of the Brexit negotiations - Lord Hague said the concerns of businesses such as Airbus and BMW "cannot be dismissed".
With Mrs May heading to the Netherlands on Tuesday for talks with Dutch prime minister Mark Rutte, Lord Hague was scathing about the way that the Cabinet infighting was playing into the hands of the EU in the Brexit talks.
"It is allowing the European Commission to sit back, make zero concessions and prepare to impose its own terms on the UK in the absence of any alternative proposals," he said.
"This is meant to be a Government negotiating a momentous international agreement not a debating society that has forgotten to impose a time limit on speeches."
He said that if the Conservatives appeared to be unable to deliver on the result of the EU referendum, public enthusiasm would be eroded while the pressure in the Labour Party to support a second referendum would intensify.
"That way lies the deepest and most bitter national division for generations and it is the responsibility of a governing party to avoid it," he said.