“Last summer, the chances of this outcome seemed minimal,” wrote Charles Grant, director of the Center for European Reform, a London-based research institute, in a briefing paper. But the odds have improved, he said, because the opposition Labour Party is now more positive about that notion if it cannot achieve its favored outcome, which is a general election.

There are plenty of obstacles, of course. Right now there is no majority in Parliament for a second vote. The Labour Party leader, Jeremy Corbyn, is not sympathetic. Holding one would almost certainly depend on the European Union granting Britain an extension on the current March 29 date for the country’s exit. And precisely what question, or questions, would be asked would provoke endless wrangling.

There are also good political arguments against it. The last vote was close — 52 percent to 48 percent — and another one would in all likelihood be so, too. That risks a polarizing and angry referendum campaign with an outcome that would be no more definitive than the first vote.

But according to several surveys, public opinion is finally shifting away from Brexit, and proponents of a rethink sense an opportunity. They want a plebiscite on the terms of an exit deal, with the option to remain, calling it a People’s Vote — a smart piece of branding designed to dispel claims that they are sore losers seeking to rerun the last referendum because they didn’t like the result.

“This was a long-shot campaign when it started,” said James McGrory, director of the People’s Vote campaign. “But the odds are getting shorter every day. All the momentum is with our campaign.”

It has been a long time coming. When Britons voted in the 2016 referendum to quit the European Union, few “remainers” believed that the decision could be changed. At first, the remain camp seemed shellshocked and, when some began to suggest a redo, it was accused of trying to undermine “the will of the people” and taunted in parts of the tabloid press as “remoaners.”