Theresa May has pledged to face down a vote of no confidence in her government, after her Brexit deal was shot down by MPs in the heaviest parliamentary defeat of the democratic era.

On a day of extraordinary drama at Westminster, the House of Commons delivered a devastating verdict on the prime minister’s deal, voting against it by 432 to 202.

The scale of defeat, by a majority of 230, was greater than any seen in the past century, with ardent Brexiters such as Jacob Rees-Mogg and Boris Johnson walking through a packed division lobby cheek-by-jowl alongside passionate remainers.

As noisy protesters from both sides of the Brexit divide massed outside in Parliament Square, the prime minister immediately rose to accept the verdict of MPs – saying she would welcome a vote of no confidence in the government.

“The house has spoken and the government will listen,” she said. “It is clear that the house does not support this deal, but tonight’s vote tells us nothing about what it does support.”

In a raucous Commons, the Labour leader, Jeremy Corbyn, confirmed he had tabled a formal motion of confidence in the government, backed by other opposition leaders, which MPs would vote on on Wednesday.

Corbyn told MPs: “This is a catastrophic defeat. The house has delivered its verdict on her deal. Delay and denial has reached the end of the line.”

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The Brexit-backing European Research Group (ERG) and the Democratic Unionist party (DUP) later announced that they would support the prime minister, making it unlikely Labour could succeed in triggering a general election.

May said that if she survived the vote on Wednesday, she would hold meetings with senior parliamentarians from all parties to “identify what would be required to secure the backing of the house”.

The prime minister’s spokesman later said May would be contacting Conservative and DUP MPs among others , but declined to say whether or not she would meet with Corbyn or the SNP leader, Ian Blackford.

He cited the example of May’s meetings with Labour MPs such as Caroline Flint and Gareth Snell about an amendment on workers’ rights, although both of those MPs eventually voted against the government. “We will approach it in a constructive spirit,” the spokesman said.

May had no plans to head to Brussels immediately, No 10 said, implying that the prime minister first needed to test what would be acceptable to MPs.

Play Video 0:37 Parliament Square cheers as Theresa May suffers Brexit deal defeat – video

Downing Street said May would approach the talks wanting to find a solution to deliver a Brexit deal that would honour the result of the referendum – suggesting she would not countenance talks with those pushing for a second referendum, or even a full customs union, which Labour has backed.

She would then make a statement on Monday, setting out how she intended to proceed. MPs would get the chance to amend the statement, and were likely to take the opportunity to try to demonstrate support for their own favoured alternatives – including a Norway-style soft Brexit, and a second referendum.

Several cabinet ministers, including Amber Rudd, Philip Hammond and Greg Clark, had pressed the prime minister at Tuesday’s cabinet meeting to pursue a cross-party solution if her deal was defeated. But Brexit-backing ministers, including Andrea Leadsom and Penny Mordaunt, urged her instead to seek revisions to the Irish backstop – and failing that, to pursue a “managed no deal”.

The former foreign secretary Boris Johnson said the crushing defeat gave the prime minister a “massive mandate” to return to Brussels and seek a better deal.

“We should not only be keeping the good bits of the deal, getting rid of the backstop, but we should also be actively preparing for no deal with ever more enthusiasm,” he said.

On Tuesday night Johnson was joined by other prominent Brexiter MPs, including John Redwood and Bill Cash, at a champagne celebration party at Rees-Mogg’s house.

Facebook Twitter Pinterest Boris Johnson leaving Jacob Rees-Mogg’s party on Tuesday night. Photograph: Sean Smith/The Guardian

Hammond moved quickly after the vote to quell business anger over the failure of May to get her deal ratified. The chancellor expressed his “disappointment” at the result in a conference call at 9pm with main business groups, including the CBI and the British Chambers of Commerce, as well as dozens of chief executives.

One source on the call said it was constructive and that Hammond’s tone was “realistic” about the damage prolonged uncertainty around Brexit was inflicting on the economy. However, Hammond was hammered by business leaders over parliament’s refusal to take a no-deal Brexit off the table. “This was the single biggest question he was asked,” said the source.

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May said any plan that emerged from the talks would have to be “negotiable” with the EU27. She earlier rejected an amendment from the Tory backbencher Edward Leigh calling for the Irish backstop to be temporary, saying it was not compatible with the UK’s legal obligations.

In Brussels, Donald Tusk, the European council president, appeared to back a second referendum soon after the crushing result for the prime minister was announced, and urged her to offer a way forward.

Donald Tusk (@eucopresident) If a deal is impossible, and no one wants no deal, then who will finally have the courage to say what the only positive solution is?

May was expected to return to Brussels within days to consult with Tusk and the European commission president, Jean-Claude Juncker. Officials said the EU was now in listening mode.

In a statement, Juncker urged the British government to “clarify its intentions as soon as possible”, and warned that “time is almost up”.

“I take note with regret the outcome of the vote in the House of Commons this evening”, he said. “On the EU side, the process of ratification of the withdrawal agreement continues”.

In a defence of Brussels’ role in the negotiations, Juncker said that the EU and the bloc’s chief negotiator, Michel Barnier, had shown “creativity and flexibility throughout” and “demonstrated goodwill again by offering additional clarifications and reassurances” in recent days.

He said: “The risk of a disorderly withdrawal of the United Kingdom has increased with this evening’s vote. While we do not want this to happen, the European commission will continue its contingency work to help ensure the EU is fully prepared.”

May, in Westminster earlier knowing that she faced a heavy defeat, made a heartfelt plea to MPs to support her, calling it “the most significant vote that any of us will ever be part of in our political careers”.

“Together we can show the people we serve that their voices have been heard, that their trust was not misplaced,” she said.

Earlier in the day, as one Conservative backbencher after another stood up to attack her painstakingly negotiated withdrawal agreement in the House of Commons, it became clear that few had changed their mind.

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May had embarked on a last-ditch charm offensive on Tuesday, holding meetings with MPs including the ERG’s Steve Baker, who said the pair had held a “constructive and substantial conversation about the future”.

Corbyn, speaking just before the vote , saidMay had “treated Brexit as a matter for the Conservative party, rather than the good of the whole country”.

He called the government’s efforts to steer Brexit through parliament “one of the most chaotic and extraordinary parliamentary processes” he had experienced in 35 years as an MP. The attorney general, Geoffrey Cox, told his colleagues that if they did not accept the prime minister’s deal, they risked condemning the UK to the chaos of a no-deal Brexit.

“It would be the height of irresponsibility for any legislator to contemplate with equanimity such a situation,” he said.

Corbyn would come under intense pressure to throw his weight behind a second Brexit referendum if May wins on Wednesday; but his spokesman said Labour did not rule out tabling another no-confidence motion at a later stage.

Labour MPs were joined by 118 Conservative rebels in voting down the prime minister’s deal, including erstwhile loyalists such as the chair of the backbench 1922 committee, Graham Brady. That was one more than the number who had backed a no-confidence vote in May’s leadership of the Conservatives in December. Under party rules, the prime minister’s victory in that vote means she cannot be challenged for party leadership again within the next 12 months.