All of Corbyn’s actions are consistent with the widely cited theory that what he wants is Britain’s exit from the EU, with the Conservatives taking the blame.

But while May openly avows her plan, Corbyn must conceal his. Brexit splits both of the U.K.’s two large parties, but Labour is, if possible, the more divided of the two.

As Tim Shipman observes in his history of the Brexit crisis, Labour is the party of both the most pro-EU and the most anti-EU voters in the United Kingdom. Meanwhile, the pro-Brexit Conservatives find themselves estranged from their natural base of more affluent, more educated voters. University graduates voted two to one to remain; high-school dropouts, two to one to leave. Those parts of Britain with the highest median incomes voted to remain; those parts with the lowest voted to leave. Brexit was a right-wing project carried out with left-wing votes.

In all democracies, there are issues that cut across party lines. The Iraq War was one such debate in the U.K. in the early 2000s; government surveillance policies were another, in the 2010s.

But those crosscutting issues—important as they were—did not change the basic grammar of the political system. Brexit potentially does.

Read: The end of the cult of sympathy for Theresa May

Nigel Farage—then the leader of the supposedly right-wing UK Independence Party—campaigned for Brexit alongside George Galloway, who in 2002 described the collapse of the Soviet Union as “the greatest catastrophe of my life.” Galloway explained himself on the radio last week: “I want Britain post-Brexit to be what it was in the swinging ’60s … when we were the cultural capital of the world … when we had a steel industry, when we had a coal industry—when we were something!”

Farage’s UKIP campaigns to “bring back the great British pub” by relaxing rules on indoor smoking and raising drunk-driving limits. Farage himself likes to be photographed cigarette in one hand, pint of ale in the other. Galloway told a rally in 2005 that when summoned before the U.S. Senate to explain his business dealings with Saddam Hussein, he had defied American law by lighting a Cuban cigar in the Capitol. Farage’s economics are kinda-sorta libertarian; Galloway’s, vaguely communist. But they both hate anti-smoking rules, and they both yearn for the Britain of 50 years ago over the Britain of today.

Meanwhile, a former Conservative cabinet official who voted Remain told me with wonder, “My daughter pinned a European Union flag pin on her backpack.” The British are not a flag-waving people. Until extremely recently, you seldom saw flags on private spaces, only government buildings. Indeed, until 2012, national law severely restricted how, when, and which flags could be displayed at all. Since that law was relaxed, visitors to England—especially England outside central London—have noticed a proliferation of flags. But not the red-white-and-blue Union flag. The flag you most often see on private homes and cars is the red-and-white flag of England.