The men vying to be Britain's next prime minister must contend with strong opinions on Brexit.Dylan Martinez / Reuters

LONDON—If the race to become Britain’s next prime minister is any indication, the ruling Conservatives are united on virtually all issues but one. Unfortunately for them, that issue happens to be Brexit—and it’s threatening to tear not only the party, but the whole country, apart.

When five of the six contenders to succeed Theresa May as Conservative Party leader—and, consequently, prime minister—gathered for their first televised debate this week, there were plenty of oddities. First, Boris Johnson, the front-runner who didn’t bother to show up, was represented by an empty podium. Then there was the debate itself, which featured strange metaphors such as the one likening Brexit negotiations to trying to get garbage into a trash can. But perhaps the oddest part of all was the realization that the men onstage—each with his own disparate view of Brexit and how to best deliver it—belong to the same party.

If this contest is any indication, the Conservative Party is more divided than ever. There is no consensus among its members of Parliament over how, or even whether, Brexit should happen. Those who want the country to leave the European Union disagree even further on when Brexit should happen, what it should look like, and how it should be delivered.

The Conservative Party has long been divided over Europe. Indeed, the Tories were split over Britain’s membership in the European Economic Area (the precursor to the European Union) in 1973. Europe dominated the 2001 leadership contest between Ken Clarke, who at the time openly supported Britain joining the EU’s single currency, and Iain Duncan Smith, a committed euroskeptic. (Duncan Smith triumphed.)

This division, however, is mostly limited to Europe. In fact, today’s Tory leadership contenders don’t really disagree on much else at all.

“There is actually very little that separates [the leadership contenders] on the more traditional lines of political conflict,” Tim Bale, a politics professor at Queen Mary University of London, told me.

The positions of the candidates, narrowed down Tuesday to five men—Johnson, Foreign Secretary Jeremy Hunt, Environmental Secretary Michael Gove, International Development Secretary Rory Stewart, and Home Secretary Sajid Javid—are largely the same on economic and social issues. All of them, for example, advocate for lower taxes. They all support more investment in education and social care. Where they fundamentally disagree, however, is on the issue that everyone seems to care most about: Britain’s impending departure from the European Union.

Virtually every candidate claims to have a solution to the Brexit impasse that has vexed the country for nearly three years. Whereas some, such as Gove, argue that the best way to salvage May’s negotiated Brexit deal with the EU is to simply remove the unpopular Irish backstop that some Brexiteers fear could tether the country to EU rules indefinitely (though May tried and failed to do just this), others, such as Johnson, have pledged to take the U.K. out of the EU by the end of October, with or without a deal.

The party’s members, who will select the next Tory leader when the final two candidates face each other in a runoff postal ballot next month, broadly support those hard-line positions. A Tuesday poll by the British polling firm YouGov found that more than half of Conservative Party members, who include not just lawmakers but also the party’s supporters, are willing to countenance almost anything—including significant damage to the country’s economy, the unraveling of the United Kingdom (in which Scotland and Northern Ireland would leave the union), and even the end of the Conservative Party—to see Brexit delivered. (The broader British population thinks leaving the EU without a deal would be a bad outcome for the country.)

“Being close to government and in some cases being in government means that some MPs are rather more realistic, perhaps, than some at the grass roots about the consequences of what some people see as crashing out of the EU,” Bale said, adding that the broader Tory membership “has become completely and utterly obsessed with Brexit to the point that it doesn’t really seem to care about anything else,” transforming what has otherwise been a relatively unideological party from “a church, and a broad church at that, into a cult.”

Still, a church—or a cult—needs a leader, and that person will need support both within the party’s grass roots and among its most senior leaders. Unlike in U.S. politics, where presidential candidates rarely serve in a rival’s Cabinet, British leadership hopefuls are more amenable to working in governments led by their former adversaries. So far, none of the Conservative leadership candidates (except Stewart) has ruled this out. “Whoever becomes the captain amongst us,” Javid said during Sunday night’s debate, “we should all unite behind that person, because that’s the only way we’re going to get a deal.”

That optimism, as May’s record of negotiating with Brussels has shown, might be deeply misplaced.

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