Talk of a second referendum in the charged aftermath of Britain's decision to leave the European Union has picked up steam here in recent days from an unlikely quarter: Mr. Brexit himself, Nigel Farage, the former leader of the UK Independence Party (UKIP).

The man who has made a career out of hating the European Union from the inside, as a member of the European Parliament, floated the idea as a way of ending the debate once and for all in a recent television interview.

"[Remain supporters] will go on whingeing and whining and moaning all the way through this process," he told Channel 5's The Wright Stuff.

"So maybe, just maybe, I'm reaching the point of thinking that we should have a second referendum on EU membership. I think that if we had a second referendum on EU membership, we would kill it off for a generation."

'We should have a second referendum … on EU membership,' says the former U.K. Independence Party leader 0:47

In a non-binding referendum on June 23, 2016, 51.9 per cent of people voted in favour of leaving the European Union. The Conservative government initiated the withdrawal process in March of last year with the aim of completing it by March 2019.

European Union politicians in Brussels — fat-cat "Eurocrats" according to Nigel Farage — were quick to follow up on his comments by pointing out that from their point of view, the door has not yet shut on the UK.

"Wasn't it David Davis" — the man responsible for negotiating Britain's exit from the EU — "who said a democracy isn't a democracy if you can't change your mind?" asked Donald Tusk, the president of the European Council at a session of the European Parliament in Strasbourg this week.

"We here on the continent haven't had a change of heart. Our hearts are still open to you," Tusk said.

The president of the European Commission, Jean-Claude Juncker, said that he hoped London had heard the message clearly that "our door remains open."

'An undermining of democracy'

Brexit supporters have reacted to the prospect of a second referendum with a certain amount of horror, some accusing Farage of seeking attention.

British Prime Minister Theresa May is engaged in difficult divorce talks with the European Union. (Stefan Wermuth/Reuters)

"It would be an undermining of democracy," said John Longworth, a former director general of the British Chambers of Commerce who also co-chairs the Leave Means Leave group.

He accused Brussels of trying undermine Britain's decision.

"The British people have voted, but of course it's normal of the EU to try and do this. They have done it in the past when peoples of Europe, for example in France, the Netherlands and Ireland, have voted against European treaties, the EU have engineered further referendums until they get the answer they want."

Longworth said he didn't want to speak for Farage, but that he assumed he spoke out of frustration at the lack of progress in exit talks. "And also a warning that there's a possibility that there will be another referendum and therefore that the Leave campaign had better be prepared for it," Longworth said.

But that is an admission of sorts in and of itself. And Remain campaigners have seized upon it.

"I think [a second referendum is] more than a slight possibility. I think it's now emerging as a real option," said the British philosopher A.C. Grayling, who chairs an umbrella organization of groups campaigning to remain in the EU.

"And from all sides of the political spectrum. It's being recognized that this is so divisive. It is by no means a done deal. As day follows day, so there's more information about the great damage that Brexit might do and the most important thing is that public opinion is swinging against it."

But there are nuances. A poll published this week by BMG Research found that 57 per cent of "those who expressed a view" would back a second referendum if British Prime Minister Theresa May fails to negotiate an exit agreement with the EU, leaving the UK to "crash out" and resort to World Trade Organization terms.

An earlier poll by YouGov published in the Guardian newspaper found 53 per cent of those polled would like a final vote on any deal. But that doesn't necessarily mean people have changed their minds about leaving the European Union or staying in.

'I'm a European citizen as well'

A straw poll on the street offered up a mixed reaction to the prospect of another referendum.

Some Brexit supporters believe the European Union has been trying to undermine Britain's decision to leave the union. (Neil Hall/Reuters)

"I think it's unnecessary," said an older man. "I think a decision's been taken and it's time to get on with it."

"I would love a second referendum," said a young woman. "I actually feel like I've lost a huge chunk of my identity because I'm not just a Brit. I'm a European citizen as well."

Theresa May, who heads up a minority government depending on support from the Democratic Unionist Party in Northern Ireland, is weaker than ever.

But any hope of a push for a second referendum from the opposition Labour Party with support from rebel Conservative MPs has been repeatedly doused in cold water by Labour leader Jeremy Corbyn. A.C. Grayling says that's because Corbyn is a Brexit supporter at heart.

The Labour leader's performance campaigning for the Remain side during the referendum was roundly criticized as apathetic and lacklustre.

"[Corbyn and his closest confidantes] are Brexiters and they do want to see a Brexit happen and they'd like to be able to pick up the pieces in their own way afterwards," Grayling said. "The great majority of the parliamentary Labour Party is Remain and the great majority of the Labour Party in the country is Remain."

Weak though she may be, May is still at the helm. And she insists there will be no "do-over."