Former prime minister Tony Blair’s brand of moderate Labor Party politics is out of fashion in Britain these days, as is Blair himself. Still, Blair is making a persistent and important point about Brexit: The British public deserves a chance to vote again on whether to leave the European Union now that the consequences of doing so have become clearer.

“I’m simply saying one very, very simple thing, which is that in 2016 you knew you wanted to get out of the European Union but you didn’t see the terms of the alternative relationship,’’ the former premier said in a recent interview with BBC Radio. “If when you see those terms, you think it is better to stick with Europe, you are entitled to have that say.’’

That has outraged some in the “leave’’ camp, but Blair’s call got some quasi-backing from an interesting quarter last week: Former UK Independence Party leader Nigel Farage, an ardent advocate of leaving the EU, said he too thinks there should be a second vote. To be sure, Farage wants one for a different reason than Blair: He believes a second victory by the leave forces would put the issue to rest once and for all.

“The percentage that would vote to leave next time would be very much bigger than it was last time round,’’ he predicted. “And we may just finish the whole thing off. And Blair can disappear off into total obscurity.’’

Actually, however, the British public seems to be having second thoughts, or “Bregrets,’’ about the June 2016 vote to leave. In an October poll, for example, 47 percent of respondents said the United Kingdom was wrong to vote that way, compared with 42 percent who called the narrow (52 to 48) leave vote the right decision. A December poll, meanwhile, found that by 50 percent to 34 percent, Britons would like to see another vote.

That’s probably because voters didn’t realize the full range of problems, dislocations, and costs that leaving the EU would bring. After all, some prominent leave voices — like, say, Boris Johnson, now the foreign minister — had assured voters they could have their cake and eat it too on Brexit. It has now become apparent that simply isn’t true.

Just how a reconsideration of Brexit would occur remains unclear. Blair says it could be either through a parliamentary election fought over that issue or through another public referendum. The first course, however, would require one of the major parties to change its stance. It’s hard to see how that would happen with the Conservatives while Theresa May remains prime minister. Labor leader Jeremy Corbyn, meanwhile, has insisted that Labor will honor the June 2016 vote.

So unless May or Corbyn is replaced, seemingly the only avenue would be for a second public vote. Some Labor MPs want their party to support such a vote, but so far Corbyn has shown no inclination to do so. Still, if the polls continue to show public regret, the referendum could become an ever more palatable option.

If so, the United Kingdom could have a debate that focuses not on the hoped-for terms of an EU exit, but the actual ones. If voters again said yes to leaving, the matter, as Farage says, would be settled once and for all. But Blair is right: With the extent of the Brexit disruption now more clear, it’s a do-over debate the United Kingdom deserves to have.