People wrapped in Union Jack flags head toward Big Ben and Parliament in London on June 26. (Odd Andersen/AFP)

Are regretful Brexit voters now saying, "Whoops?"

If you've been reading about Britain's vote to leave the European Union over the past few days, you may be reaching that conclusion. There seem to be plenty of pro-Brexit voters who now feel they've made a terrible mistake. “I wish we had the opportunity to vote again,” one anti-E.U. voter told ITV news. "I didn't think my vote was going to matter too much because I thought we were just going to remain," another told the BBC.

One man who spoke to The Washington Post even said he'd signed a petition for a new referendum just a few hours after he voted to leave the E.U. "I was swayed by the rhetorics," Antony Kerin explained of his original vote. "If I had thought this through, I would have voted to stay in. I would certainly do so now."

Such stories have quickly become viral hits among online readers. In the spirit of Brexit, these attitudes even have their own media-friendly nickname: Bregret or Regrexit. They seem to confirm many anguished "remain" voters' belief that the Brexit campaign was based on lies and fear-mongering. It provides hope that perhaps a second referendum would not only set Britain back on track but also be the morally justifiable thing to do.

Unfortunately for those people, the data we have on Bregretters is not convincing.

Although there is no shortage of "leave" voters expressing regret to journalists, more than 17 million Britons voted to leave the E.U. A few dozen — heck, even a few thousand — regretful "leave" voters are not statistically significant: The difference between the "remain" and "leave" camps was more than 1 million. At best, what we have right now are individual anecdotes. What we'd need to get an accurate picture of Bregret is really representative data from polling companies.

We should soon have that. A number of polling companies are working on post-vote surveys that ask "leave" voters how they feel about the result. At the time of writing, it appears that only one company, Survation, has published anything like this. In a post-referendum poll conducted Thursday and Friday, Survation asked "leave" voters whether they regretted their vote. About 7.1 percent came out as Bregretters. That number isn't totally insignificant, but it isn't a game-changer: 4.4 percent of "remain" voters also said they wished they had changed their vote.

Of course, there will be plenty of hand-wringing about whether such a poll could really be accurate. Britain's pollsters have been notoriously inaccurate over the past few years, and only a few had correctly guessed the scale of Thursday's "leave" vote before the referendum. Polling experts might also take some issue with the fact that the Survation poll was an opt-in one rather than based on a probability sample (Chris Hopkins of Survation says his company could feasibly re-contact a large number of people who had indicated prior to the election that they would "leave" for a more vigorous poll, though it has no immediate plans to).

But whatever you think about the limitations of polls, they provide a better snapshot of a country than a random interview with a journalist.

For a long time, many involved in British opinion polls have pointed to the "shy Tory factor" — that is, the tendency of right-wing voters to not declare their true voting intentions to pollsters. Some have reasoned that this is because right-wing voters can be slightly ashamed to publicly reveal how they voted. It's not hard to imagine that some "leave" voters, faced with a global media that deems their decision unimaginable and foolish, might tell a reporter that they regret their vote. Some of those people may well mean it, some may not.

Extrapolating any further right now would be foolish — and may well betray an "elite" condescension that many Brexit supporters have already complained of.

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