Hardcore Brexiteers, such as former foreign secretary Boris Johnson, cheered the result as increasing the chances of Britain leaving the European Union with no deal and no compromises — or with a much, much better deal than May or E.U. leaders say is realistic. At the same time, those who want to see a second referendum on Brexit, and who want to stay in the union, think May’s loss gets them closer to their goal.

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The political turmoil heightened fears among European leaders that Britain will crash out of the bloc in a chaotic, no-deal departure that would have harsh economic and humanitarian consequences on both sides of the English Channel.

“The risk of a disorderly withdrawal of the United Kingdom has increased with this evening’s vote,” European Commission President Jean-Claude Juncker said in a statement. “While we do not want this to happen, the European Commission will continue its contingency work to help ensure the EU is fully prepared.”

In the House of Commons on Tuesday, May stood almost alone, flashing defiance and frustration, as many in her own party abandoned their leader.

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Historians had to go as far back as the Victorian age to find a comparable party split and parliamentary defeat — to Prime Minister William Gladstone’s support for Irish home rule in 1886, which cut the Liberal Party in two.

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“The events in Parliament today are really quite remarkable,” said University of Cambridge political historian Luke Blaxill. “This doesn’t happen.” Meaning, usually British parties fight with one another in Parliament — but members don’t tear their own parties apart.

Jeremy Corbyn, the opposition Labour Party leader, called the loss “historic” and said May’s routine of “delay and denial” had led to disaster. “She cannot seriously believe after two years of failure she is capable of negotiating a good deal,” Corbyn said.

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He then introduced a motion of no confidence, to be debated and voted upon Wednesday.

Afterward, leaders of Northern Ireland’s Democratic Unionist Party, which props up May’s minority government, announced that they would support the prime minister, thereby making her ouster unlikely.

Rob Ford, a professor of politics at Manchester University, said these were indeed strange times. “Normally, if you were looking at a defeat of 50-plus votes on the No. 1 item on the government’s agenda, then that would be it. Game over. The prime minister would be gone, and the government would probably fall immediately. But that’s clearly not going to happen,” Ford said.

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May called Tuesday’s vote in Parliament the most important in a generation. She told lawmakers that the choice was plain: support her imperfect compromise deal — the only one Europe will abide, she stressed — or face the cliff edge of a no-deal Brexit.

Staring directly at Corbyn, May said anyone who thought they could go to Brussels and get a better deal was deluding themselves.

But the vote against her plan was decisive.

Moments after the result came in, May said, “The government has heard what the House has said tonight.”

She has until Monday to return with a Plan B. Her office has been tight-lipped about what alternatives she might offer. May said she would reach out to members of Parliament to find out what kind of Brexit deal, if any, they would endorse.

“What Theresa May does now will become less and less relevant to what outcome we get. The key thing to be watching is what Parliament does next and what Labour does next,” Ford said.

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Other European leaders, who expected the deal to fail, were stunned by the scale. Yet they said they saw little they could do to try to ease any agreement through the British Parliament.

“Maybe we’ll make improvements on one or two things,” said French President Emmanuel Macron. “But I don’t really think so, because we’ve reached the maximum of what we could do with the deal, and we won’t, just to solve Britain’s domestic political issues, stop defending European interests.”

Guy Verhofstadt, the Brexit coordinator for the European Parliament, sounded especially frustrated. “The House of Commons today said they don’t want this deal. I want to know what deal the House of Commons really does want. Because otherwise you can’t make an agreement.”

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At least one prominent voice suggested that Britain might reconsider its divorce effort altogether. “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?” European Council President Donald Tusk tweeted.

Britain could ask to postpone Brexit beyond March 29 and try to buy more time to work out its problems. An extension would require unanimous consent from the remaining E.U. countries. “It creates a great deal of uncertainty and worries,” Macron said.

In the chamber at Westminster, the debate before Tuesday’s vote was impassioned and divided. As members hooted and jeered, the speaker gaveled them to be quiet, complaining of the “noisy and unseemly atmosphere.”

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“The House must calm itself. Zen!” John Bercow shouted.

Rising Labour Party star David Lammy recalled how he had confronted constituents who sympathized with the violence carried out by London rioters in 2011. Now he said he felt the same duty to confront his neighbors on Brexit.

“Why? Because we have a duty to tell our constituents the truth, even when they passionately disagree,” Lammy said. “Brexit is a con, a trick, a swindle, a fraud.”

In another emotional speech, Geoffrey Cox, a Conservative lawmaker and the attorney general, urged the chamber to back May’s deal. “What are you playing at? What are you doing? You are not children in the playground. You are legislators, and it is your job. We are playing with people’s lives,” Cox said.

Outside Parliament, the scene was raucous. Thousands of protesters, many in costumes, gathered to shout at each other — illustrating how unsettled Brexit remains more than two years after voters opted in a 2016 June referendum to leave the E.U.

Brexiteers banged drums and rang a “liberty” bell, while pro-E.U. demonstrators handed out “Bollocks to Brexit” stickers in Parliament Square beside two huge video screens set up for the live broadcast of the final speeches and the vote.

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Jeff Wyatt, 54, a pro-Brexit voter, held aloft a placard that accused May of treason. Another man in the crowd suggested that the prime minister should face the executioner’s ax.

“For the first time in the history of my country, we’ve got Parliament against the people,” Wyatt said, gesturing at the Palace of Westminster.

Monika Wolf, 57, was clutching an E.U. flag and a Union Jack. She moved to Britain from Germany in 1981 and studied and raised her children here. In an ideal world, she said, Brexit would be stopped. She hoped to see “more statesmanship from the big parties — they both talk about bringing the country together, but so far they haven’t done anything at all to make that happen.”