Brexit campaigner Nigel Farage leaves a meeting at the European Commission headquarters in Brussels on Jan. 8. (Francois Lenoir/Reuters)

In the months since the 2016 Brexit vote, some who backed leaving the European Union have shown a certain amount of remorse.

One report, published Wednesday by Demos, a think tank, found that a “relatively significant proportion” of voters who opted to have the United Kingdom exit the E.U. are starting to change their minds. Focus groups, the authors write, “distinctly captured an emergent sense of regret amongst a relatively significant proportion of leave voters. We saw a growing anger at having been forced to take such a momentous decision, without sufficient understanding of the consequences.”

That bitterness — along with the feeling that exit negotiations with the E.U. are not playing out in favor of the U.K. — has prompted some key “remain” supporters, including former prime minister Tony Blair, to call for a second vote. Labour leader Andrew Adonis said a second vote would overturn Brexit. Liberal Democrats made a second “exit from Brexit” vote a plank of their 2017 campaign.

Today, that bid found an unlikely ally: Nigel Farage, the former head of the U.K. Independence Party and the prime architect of Brexit.

In an interview on “The Wright Stuff,” a talk show, Farage suggested that a second referendum would put the issue to rest, claiming a second win for the “leave” side would kill the issue “for a generation.” Otherwise, he cautioned, “remain” supporters will “go on whingeing and whining and moaning all the way through this process.”

“Maybe, just maybe, I'm reaching the point of thinking that we should have a second referendum … on E.U. membership,” he said.

Farage predicted that the percentage of voters choosing to leave the E.U. would be “very much bigger than it was last time round” if a second referendum were held.

Polling doesn't quite bear that out. According to a tracking poll conducted in December, 46 percent of Britons back remaining part of the E.U. while 43 percent say they want to stick with “Brexit.” The rest were undecided.

That doesn't mean, however, that a majority want a second vote. Just 37 percent of U.K. voters think there should be a second vote once negotiations with the E.U. finish up, according to a tracking poll by What UK Thinks. Nearly half of those surveyed, 49 percent, say there shouldn't be a second vote.

Farage's change of heart echoes comments from the co-founder of Leave E.U., Arron Banks, who said recently that to avoid sleepwalking into a “faux Brexit,” the only option is to “go back to the polls and let the people shout from the rooftops their support of a true Brexit.”

Farage's colleagues are not so keen on a second vote. Henry Bolton, who was elected UKIP leader in September, said a second referendum would be “damaging to the nation.” Gerard Batten, a spokesman for UKIP, called Farage's comments “totally unhelpful and unnecessary.”

Prime Minister Theresa May had voted to remain in the E.U., but she also is opposed to holding another referendum on the issue. “We are not having another referendum, and that's absolutely crucial,” she said in October.