Those reports raised the prospect that the prime minister would delay the vote to avoid an embarrassing defeat in Parliament. And support for a second referendum on Britain’s departure appeared to be gathering steam among both Labour and Conservative lawmakers.

The grievances that fueled the Brexit vote are simmering once more. Disappointment may well inject new energy into the far right, said Tim Bale, a professor of politics at Queen Mary University of London.

“The prospect that Brexit would fix everything was enough for all but the most rabid xenophobe,” Mr. Bale said. “When people realize that it won’t stop the economy sucking in people to do the jobs that Brits can’t or won’t do, that it won’t stop people coming in via family reunification or asylum provisions, and that it won’t do anything to send home the millions of people here already, then there will be trouble.”

He added, though, that any embrace of violence or racism would consign the U.K. Independence Party, which played a major role in building support for leaving the bloc before the 2016 referendum, to “marginal irrelevance.”

Already, the party has begun a drift toward the political edges, appointing Mr. Robinson, whose real name is Stephen Christopher Yaxley-Lennon, as an official adviser.

That has spurred resignations from the party and prompted fears that the far right, already emboldened by the referendum result, would capitalize on frustrations with Mrs. May’s deal. Many of those taking part in the “Brexit Betrayal” march said that job loss was their central grievance.

“I’m in construction, and in seven years on building sites I’ve worked with four English builders,” said Lee Windsor, 51. “The rest of them are from Lithuania, Latvia, Estonia, wherever. The wage difference is: I pay tax, and they get paid in cash.”