LONDON — “Hello, and welcome aboard the People’s Vote express from Bristol Temple Meads to London Paddington,” Sally Patterson, 23, said into the microphone, before handing it back to the conductor.
With that, a chartered train carrying students departed on Saturday morning for a march in London that is expected to draw hundreds and thousands of people, all of them agitating for Britons to be given another vote on the country’s plan to leave the European Union.
The idea that the British could still be debating in late March a reversal of the coming split from the bloc, a process known as Brexit, once seemed far-fetched. The country had been scheduled to leave on March 29.
But Parliament remains deadlocked. The left and right despise Prime Minister Theresa May’s plan. And even as deadlines were pushed back and European leaders preached patience with their counterparts in London, the prospect of a calamitous no-deal Brexit looms closer every day.
The way the organizers of the march on Saturday see it, there is one way out of the impasse: Give Britons another chance to vote on whether to leave the European Union. The country voted by a 4 percent margin to extract itself from the bloc in a referendum in 2016.
“Our demand is a simple one: that any Brexit is put the people so that we can have the final say,” the People’s Vote coalition said on its website.
Organizers hope to draw hundreds of thousands of supporters during the day. People began marching at midday on Saturday in London after arriving by bus and train from across Britain, posting images of their journeys on Twitter. On the train from Bristol to London, where Ms. Patterson was welcoming supporters, another organizer asked people in a video posted on Twitter to walk to Coach F to make placards.
Some of the estimated three million European Union citizens living in the country, many of whom say they resent not having been given a chance to vote on the issue, were expected to take part, as well.
The demonstration was a stark contrast to an ongoing march “against Brexit betrayal.”
A few dozen Brexit supporters — backed by Nigel Farage, the former leader of the euroskeptic U.K. Independence Party — set out on March 16 in Sunderland, in northeast England, a community that voted in favor of Brexit. They paid 50 pounds each for kit and accommodation along the route, and have been walking south toward London ever since, headed for a rally on March 29 where organizers hope many more Brexiteers will join them.
Hanging over the anti-Brexit march in London was the reality that a second referendum remains unlikely. Opposition Labour Party leaders, who have long dithered over a second referendum, have never energetically backed the idea.
There was also the question of how a pro-European campaign tainted in 2016 by its association with the political elite of London could create a new message three years later, one that appealed to smaller towns and cities in the English North and Midlands.
Protesters have repeatedly gathered outside Parliament since the 2016 referendum, carrying messages that included support for the country’s membership in the European Union and demands for a hard exit from the bloc.
A week after the referendum, thousands gathered in London. Waving European Union flags, marchers expressed their incredulity at the result and said the hoped that it would be reversed.
As Mrs. May repeatedly failed to persuade enough lawmakers to back her plan, there have been some signs of growing support for the idea of a second referendum, though pollsters’ findings have varied widely depending how the question is asked and backing in Parliament remains sparse.
Mrs. May’s recent trip to Brussels led to an extension of the Brexit deadline, giving British lawmakers until April to approve her deal. If it is rejected, the options include a chaotic British exit without an agreement with the European Union or a longer extension of the deadline.
The most likely form a second referendum would take is a choice between the prime minister’s exit deal and remaining in the European Union. Many polls show that Britons have now gone from mostly thinking that Britain was right to leave Europe after the referendum to mostly thinking the opposite.
Support for a public vote has also grown, according to a mid-March poll by YouGov for the People’s Vote campaign, with the option of staying in Europe favored over Mrs. May’s divorce deal or a no-deal exit. But the latter prospect has also grown more popular among Brexit supporters.
In October, a march for a second referendum gathered what the organizers said was nearly 700,000 protesters in London. A British newspaper later obtained a local government estimate that put the crowd at a still-considerable 250,000 people.
The rancor on both sides has split families and resulted in lost friendships.