Emily Thornberry, U.K. Shadow Foreign Secretary | Ian Forsyth/Getty Images Labour’s Thornberry demands referendum on any Brexit compromise British shadow foreign secretary says public should be given option to stay in EU.

LONDON — Emily Thornberry, the U.K. shadow foreign secretary, demanded any Brexit deal between her party and the government be put to a second referendum as she suggested Labour MPs from Leave-supporting constituencies were “misunderstanding” their own voters.

Speaking at a live taping of POLITICO’s EU Confidential podcast in London on Sunday, Thornberry said any deal agreed between Prime Minister Theresa May and Labour leader Jeremy Corbyn would prove controversial.

“The question will be — is this what anybody wants? Or do we end up with a compromise that just makes everybody unhappy?” Thornberry said. “I think whatever it is, it will be controversial. And I think that in those circumstances, it’s right for us to be saying to the British people: 'During that referendum, did you vote for this? Do you want this? When you said you wanted to leave, did you want to leave like this?'”

She said the public should be asked the question: “Is this what you want or do you want to remain?”

Asked whether a Labour-Tory deal and a referendum should be bundled together in one package in parliament — which would make a public vote far more likely to go through — rather than being subject to separate votes, Thornberry said: “I think that the two things need to go hand in hand.”

Labour is split over whether any deal should go to a referendum. Some in the party argue that such a strategy would be highly risky, particularly in Labour constituencies that voted for Brexit.

Those MPs and officials worry that holding a referendum that could result in the U.K. staying in the EU would be seen as a betrayal by Brexit-backing Labour voters.

But Thornberry suggested some in the party were laboring under a misunderstanding. She argued that even in Labour constituencies where a majority voted to leave the EU, many of those votes came from Conservatives.

“I think there’s a fundamental misunderstanding sometimes. Because sometimes people think that they come from a ‘Leave seat’ and a ‘Leave seat’ might be a seat where 65 percent of the population in the referendum voted to leave," she said at the taping, part of Podcast Live, a day of live recordings of political podcasts in London.

"But the reality for a Labour MP is that if 65 percent voted to leave, what proportion of the 35 percent, the Remainers, voted Labour?” Thornberry added. “I think it’s important sometimes for people to kind of just remember and to segment their vote and to remember that the vast majority of Labour voters want to remain.”

Thornberry also said: “For people to think ‘the decisions that I make must be made on the basis that I come from a Leave seat,’ and just like, you know, for me, if I was to make a decision on the basis that my seat is a Remain seat, that would be wrong. What you have to do if you’re in the national leadership is do what’s right for the country as a whole.”

The special episode of EU Confidential featuring Emily Thornberry will be available to stream and download soon.