Facing an embarrassing defeat, British Prime Minister Theresa May on Monday abruptly postponed a critical vote in Parliament on her proposal for leaving the European Union. Earlier in the day, an EU court ruled that Britain could reverse its withdrawal unilaterally before March 29, 2019, the date of its scheduled departure. The day’s events were a red flag for hard-right British supporters of Brexit, who had marched Sunday against a “Brexit Betrayal” and warned that Britain risks civil unrest if Brexit is cast aside. The march was organized by UKIP, a populist anti-EU party. It’s seeing renewed support, especially amid talk of a second Brexit referendum that could reverse the first. But a new UKIP leader who advocates an anti-Islam agenda may end up costing the organization support. Even before Sunday’s rally, which featured Nazi-era signs and violent iconography, former UKIP leader Nigel Farage announced his resignation from the party he co-founded. Robert Ford, a professor of politics at Manchester University, says UKIP’s decision to lurch rightward appears poorly timed. “They’ve marginalized themselves really at the moment when they could have come back into the conversation,” he says.

They came on buses and trains, carrying British and English flags and homemade signs. Elderly veterans wore their uniforms and medals. Young men handed out political flyers.

As the crowd swelled under leaden skies, a wail of bagpipes signaled the start of the march. A march for Brexit – a clean break from the European Union – and against Prime Minister Theresa May and any other politician who dares to defy the 17.4 million Britons who voted in 2016 to leave. “Hard Brexit, Traitor May,” read one flag.

Sunday’s pro-Brexit march by UKIP, a populist anti-EU party, was modest in numbers, less than 5,000 at its peak, and easily outnumbered by a counter-protest by left-wing groups. But it was the first stirrings of what could be a broader backlash to an idea now gathering force in Britain: that the exit from the EU should be delayed or shelved altogether.

On Monday, an EU court ruled that Britain could reverse its withdrawal unilaterally before March 29, 2019, the date of its departure. Hours later, Ms. May abruptly postponed a critical vote due Tuesday on her proposal for leaving the EU after failing to persuade lawmakers to support it. She vowed to reopen talks with EU leaders, but didn’t set a deadline for another vote.

This political impasse has fueled cross-party calls for a second referendum as a way out.

That prospect is a red flag to the men and women who marched Sunday against a “Brexit Betrayal” that many say would be the final straw. Some invoked the yellow-vested rioters in France, echoing the warnings by May’s allies that Britain risks civil unrest if Brexit is cast aside.

Street battles a la française are not very British, says John Ware, a retired joiner from the Midlands who joined Sunday’s march. “We’re too polite,” he says. But such forbearance has its limits. “When pushed too far, we will react,” he says.

Anti-Islam agenda

Having faded away after the initial Brexit referendum, which fulfilled its mission, UKIP now has a cause to reanimate its base. Added to this combustible political mix is a tilt by UKIP toward an anti-Islam agenda under a new leader who has embraced far-right celebrities.

This time, UKIP is channeling a more overt nativism, akin to the far-right populist parties that have steadily gained power across Europe, from Sweden to Italy to Germany. And it has cast aside its fig-leaf of respectability by giving a platform to militant cultural warriors. It’s a move that may cost it support as it animates a more extreme base.

Matt Dunham/AP Brexit supporters hold placards and protest across the street from the Houses of Parliament in London, Monday, Dec. 10, 2018.

“The march was an attempt to weaponize Brexit by the far-right in the UK,” says Nick Ryan of Hope Not Hate, an anti-racist monitoring group.

Even before Sunday’s rally, which featured Nazi-era signs and violent iconography, former UKIP leader Nigel Farage announced his resignation from the party he co-founded. Other UKIP members of the European parliament have followed suit.

This exodus underlines the tensions within UKIP and may sap its ability to harness broader pro-Brexit anger, says Robert Ford, a professor of politics at Manchester University who studies populist parties. Its decision to lurch rightwards appears poorly timed, he says.

“They’ve marginalized themselves really at the moment when they could have come back into the conversation,” he says.

Still, the febrile politics of Brexit, and the ruptures that any reversal could cause, make it impossible to write off UKIP or, potentially, another insurgent party. Mr. Farage reportedly has been in talks with anti-EU donors about setting up another party, possibly with defections from May’s right flank.

In the event of a halt to Brexit, “I think it’s plausible we’ll see a severe amping up of all the kinds of polarization we’ve seen in the last few years,” says Mr. Ford.

An opening for UKIP?

When Britain went to the polls last year, UKIP got less than 2 percent of votes, down from 13 percent in 2015, its high water mark. While its previous surge in the polls didn’t translate into seats in Parliament, due to Britain’s winner-take-all system, it rattled the center-right Conservative Party, whose then leader David Cameron promised to hold a referendum on EU membership.

Recent polls put UKIP closer to 8 percent. Should the main parties swing behind a second referendum on Brexit, UKIP is certain to spy an opening.

Writing in the pro-Brexit Sun tabloid newspaper last week, columnist Rod Liddle savaged the “treachery and betrayal” of May’s government. “The people of the UK will not forget the names of those who have sold us down the river. And one day, sure enough, we’ll have our revenge.”

How much such blood-curdling rhetoric is political theater is hard to gauge. But a reversal of Brexit would take Britain into uncharted waters.

Last week, May warned members opposed to the proposal that to hold another referendum after promising that the last one would be binding would be undemocratic.

“This House voted to give the decision to the British people and this House promised that we would honor their decision,” she said. “If we betray that promise, how can we expect them to trust us again?”

On Monday, amid jeers from opposition MPs, May again pushed back. “If you want a second referendum to overturn the first, be honest that this risks dividing the country again,” she said.

‘We’re not racists. It’s about control.’

Among the speakers at Sunday’s UKIP gathering was Tommy Robinson, a controversial anti-Islam activist with a criminal record. Some marchers said they didn’t agree with his inclusion and wanted to stick to defending Brexit, including stricter curbs on immigration.

“We’re not racists. It’s about control,” says Steve Burn, echoing a slogan of the Leave campaign. He complained that Mr. Robinson, whose real name is Stephen Yaxley-Lennon, was hijacking Brexit for his own campaign against Islam.

Brexit supporters bristle at claims that they were misled into voting to leave the EU against their economic interests. Much of the stronger support for Brexit comes from deprived districts in England and Wales that have suffered decades of deindustrialization and social dislocation.

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Like others interviewed at Sunday’s march, Maureen McCoy said this was her first time at a political protest. That morning, she had joined 45 others from Wigan in northwest England on a five-hour bus ride to London. She carried a handmade sign, “This Stupid Northerner Knew What She Was Voting For.”

Pausing to find her friends in the crowd, she shook her head at May’s fitful negotiations. “We just need to get out. It was a straightforward in/out referendum,” she says.