Theresa May is being warned by cabinet colleagues that a shift towards a harder Brexit will hasten the break-up of the UK, amid a renewed attempt by Brexiters to secure a clean split from the European Union.

With senior Tories warning that the prime minister now risks a diplomatic calamity on the scale of the Suez crisis, following her disastrous Salzburg summit, she is facing a renewed campaign among ministers and influential backbenchers to ditch her current plans and back a looser free trade deal with the EU.

However, some cabinet ministers are concerned such a shift will effectively place a border between Northern Ireland and Britain and put it “in the departure lounge from the UK”. Cabinet sources are also warning that such a move would reignite the debate about Scotland’s place in the UK and further unravel the union. “Nobody voted Brexit to break up the UK,” one minister said. Another said: “Those advocating [the free trade deal] approach need to face up to the consequences for the union.”

Some Tory aides are said to be so worried about the lack of support for May’s current Brexit plans that they fear another snap election will be needed before the end of the year. Downing Street sources categorically denied that such an option was being considered in No 10.

Last night, May again attempted to calm the warring factions in her party, calling for “cool heads”.

“It is time to hold our nerve,” she said. “I have said many times that these negotiations would be tough, and they were always bound to be toughest in the final straight.” She also accused Labour, Lib Dem and SNP figures of “actively undermining the UK’s negotiating position” in their talks with the EU.

May’s diplomatic miscalculation last week led senior Tories to compare it to the Suez crisis, the foreign policy blunder of 1956 that destroyed Anthony Eden’s premiership. A major Tory donor said: “This will accelerate business concern even further. This ends up with us suffering a series of quite cataclysmic events.

“It is like the Suez crisis. You just don’t know what the unintended consequences will be. The next three weeks could change everything. The Suez crisis went on for months and this is up there with some of the great turning points in British political history.”

Since May’s Chequers deal was rejected in humiliating fashion by EU leaders last week, momentum has been building once again among some Tories behind the idea of securing a free trade deal, similar to that given to Canada. A report by the Institute of Economic Affairs backing such an idea will be launched on Monday and is expected to receive significant support from Tory MPs. Jeremy Hunt, the foreign secretary, yesterday refused to rule out pursuing a Canada-style deal, but warned it would not solve the Irish border issue.

On Saturday, Nigel Farage and David Davis, the former Brexit secretary, both took part in a rally in Bolton calling for May to “chuck Chequers”. Davis said: “If you think you can bully this country, you really should read some history books.”

While cabinet ministers continue to back the Chequers proposals in public, many acknowledge that they would have to be seriously reworked to have any hope of being backed by Brussels. Even then, it is not clear that a majority of MPs will back such an outcome.

Those in cabinet advocating a shift towards a Canada-style deal believe it would not lead to a border in the Irish Sea. They predict that with an acceptable Brexit deal in the offing, the EU will agree to soften its line on border checks. “This is the way we have to go,” said a source.

The Tory turmoil has led Labour to hope that an election may be the ultimate outcome. However, pro-Remain Tory MPs warned Labour that while they would never vote to topple the government, they might be persuaded to back a second referendum on Brexit should Labour support one.

Guto Bebb, the former Tory defence minister, said: “Conservative MPs will not vote to bring down a Conservative government. For the Labour leadership to continue peddling the myth that they will is frankly bizarre. If there is a Brexit deal and the government cannot secure support in parliament, the options will then be crashing out with no deal – which nobody voted for – or putting the matter back to the public through a people’s vote.”

Anna Soubry, another Tory Remainer, said: “If, as seems likely, parliament becomes gridlocked over Brexit, the only credible way out that I can see will be a people’s vote. The idea that Conservative MPs would instead vote with Labour to bring down the government is a fantasy.”

Tory MP Heidi Allen said: “It’s not just Conservative MPs who wouldn’t support calls for a general election, a significant number of Labour MPs wouldn’t, either.”