Dominic Grieve, a leading Conservative opponent of Brexit, has predicted that up to a dozen ministers – including six from the cabinet – could resign if Britain leaves the EU without a deal.

“Many of them have made representations directly to the prime minister indicating their concern and telling [her that] if by the end of February there is no deal that has been got through the Commons we ought to extend [the article 50 process],” Grieve said.

He said if Theresa May refused to do that, ministers would face a “very difficult choice”, and unless MPs worked together to prevent no deal happening, it could still happen. “In the end it could be so chaotic it might even happen by accident.”

He told BBC Radio 4 Today’s programme: “The irony of all this is that most of us in the Conservative party are sufficiently united to want to try to operate a coherent government. But the truth is we’re finding it harder and harder to do.

“It starts to bring into question whether in fact the government is able to operate in the national interest at all. We are facing a great crisis and we are not really looking at all the options for trying to resolve it.”

His comments came as Andrea Leadsom, the leader of the Commons, defended May’s attempts to pass a Brexit deal, the morning after MPs inflicted another defeat on the government’s attempts to seek changes to the backstop.

Leadsom said Thursday’s vote did not mean MPs had withdrawn their support for May, despite a fifth of Conservatives refusing to back their leader. “The prime minister carries on,” she said. “She will continue to seek those legally binding changes to the backstop that will enable parliament to support our deal.

“Yesterday was more of a hiccup than the disaster that is being reported.”

May was not present at her latest humiliation in the Commons, in which the Eurosceptic European Research Group, led by Jacob Rees-Mogg, abstained on a government motion that appeared to rule out a no-deal Brexit. As a result, the motion was defeated by 303 votes to 258.

Leadsom, however, sought to exonerate her Eurosceptic colleagues in the ERG, instead laying the blame on the Labour party for voting against the deal.

“The one problem with last night’s vote is that it allows the EU to continue with this pretence that they don’t know what we want,” she said. “They do know what we want. “It was quite clear from the vote two weeks ago that what parliament wants to see is the issues around the backstop resolved in a legally binding way.

“What last night’s vote was quite clearly about was the Labour party playing politics because they decided to vote against what was a very unharmful motion, merely setting out that the prime minister needs more time to deal with the issues that the house raised two weeks ago.

“The ERG abstained because they didn’t like the prospect that it might suggest they were supporting taking no-deal off the table.”

A Foreign Office minister, Alistair Burt, made clear his unwillingness to accept a no-deal departure, telling hardline Brexiters in a tweet: “We are not leaving without a deal. If you want to leave, you’d better agree one. In the next fortnight would help.”

In Brussels, diplomats said the result confirmed that the prime minister was incapable of commanding the support of her party on key votes, and that she needed to work across parties. “No one can take any good from this,” said one diplomat.

The vote is not binding but it appeared to be a show of strength by about 60 MPs in the ERG, which included Boris Johnson, the former foreign secretary; Dominic Raab, the former Brexit secretary; and Steve Baker, the former Brexit minister. A small number of pro-EU MPs also refused to back the motion.