A furious Theresa May rounded on her cabinet ministers on Thursday, upbraiding the four cabinet ministers who defied a three-line whip and abstained on a no-deal Brexit motion on Wednesday night.

In a cabinet meeting described as “difficult” and “tense” the day after a chaotic night in parliament, the prime minister angrily criticised the rebel ministers as well as the whole cabinet for its tendency to leak – only for business secretary Greg Clark to leap to the rebel group’s defence.

The other rebels were the Scottish secretary, David Mundell, the work and pensions secretary, Amber Rudd, and the justice secretary, David Gauke.

After the confrontation, Geoffrey Cox, the attorney general, urged cabinet ministers to unite and focus on efforts to win over the Democratic Unionist party ahead of the third meaningful vote.

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Strenuous diplomatic overtures have been made to the DUP, whose leader Arlene Foster suggested on Thursday that she was ready to broker a deal to secure the party’s backing.

Foster, who is visiting Washington for an event she attended with the Irish prime minister, Leo Varadkar, said her party was back in talks with the government, and that she believed a compromise would be found in the final days.

“We want a deal, we’ve said we want a deal, and we’re talking to them around that,” Foster told the BBC. “We hope that can be the case, because nobody wants to leave without a deal. We know that is bad for the whole of the United Kingdom and we want to make sure that we get there.”

“When you come to the end of the negotiation, that’s when you really start to see the whites of people’s eyes and you get down to the point where you can make a deal,” Foster said.

May’s spokesman said it was a “productive, open and honest discussion” at the political cabinet on Thursday afternoon, and that the “cabinet collectively agreed to redouble their resolve on working to deliver on the result of the referendum to leave the EU, by securing support for a deal”.

Later on Thursday, eight cabinet ministers, including the Brexit secretary, Stephen Barclay, voted against the prime minister’s plan to delay article 50, but Downing Street made clear that all would be bound by collective responsibility to support the plan.

Sources said the prime minister’s anger at cabinet was not reserved for her rebellious ministers, however, scolding her entire cabinet for the scale of leaks, suggesting that some ministers were self-serving and concerned only with their leadership prospects.

One cabinet source described the atmosphere as “difficult and uncomfortable” and said May had made it very clear how angry she was at the scenes on Wednesday night.

“It was quite tense in the room, but people did need to clear the air, the conversation needed to be had,” the source said. “The remainer ministers said their piece and they got what they thought they would get – a dressing down.”

Clark, the business secretary, attempted the longest explanation of the group’s actions, saying that ministers had been promised a free vote in order to vote down no deal but then found themselves being ordered to vote the other way. “They are mostly angry about the cock-up,” one source said.

But there was little appetite for the explanation, with the chief whip Julian Smith abruptly leaving the room. “No one was much in the mood to hear about it,” one source said.

At the end of the meeting, it was Cox who appealed for unity, saying he could understand how people could feel marginalised. “His intervention, probably because it came from him, seemed to soothe a lot of nerves,” one cabinet source said.

However, a possible route to winning over both the DUP and some members of the hard-Brexit European Research Group appeared unlikely on Thursday night as the “star chamber” of Brexiter lawyers appointed to scrutinise the attorney general’s rulings on the backstop rejected his latest supplementary legal advice.

The Telegraph reported that Cox believes the UK can extricate itself from the backstop under the terms of the Vienna convention if it began to have a “socially destabilising effect on Northern Ireland”. But the lawyers said “given the high burden that a state must meet to use it, and given the extreme reluctance of international courts and tribunals to accept it” the Vienna convention route “supplies no assurance whatsoever that the UK could terminate the withdrawal agreement in a lawful manner”.

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Martin Howe QC, the only non-MP in the “star chamber” had earlier said the idea was a non-starter.

Howe told the Evening Standard that the use of the convention – the international agreement that lays down the rules about treaties – required a “radical change of circumstances” and said that the international court of justice had considered “the fall of the Soviet Union, disappearance of the Warsaw Pact and dissolution of Czechoslovakia, were not sufficient to satisfy this ground”.