It’s tempting to conclude that because pro- “remain” parties did better in the United Kingdom’s European parliamentary elections than those pushing for a no-deal Brexit, the country has made up its mind to reverse the result of the 2016 referendum. If only it were that simple.

The vote showed the public is, if anything, more polarized. The Liberal Democrats, once the third party in Britain but destroyed after a period in coalition government with the Conservatives, rose from the ashes to overtake the Labour Party. They won just over 20 percent of the vote with an avowedly remain campaign.

Add the Lib Dems’ results to those for the other firmly remain parties — the Greens (12 percent), the new Change UK Party (3.4 percent) and the pro-remain Scottish Nationalist Party (3.6 percent) — and nearly 40 percent of the vote was in favor of staying in the European Union. That’s more than the 35 percent combined vote of Nigel Farage’s Brexit Party (32 percent) and his former UKIP grouping, both of which pushed for a no-deal exit.

This shows that there is no center in British politics when it comes to Brexit. Instead of the old left-right distinctions that allowed the two big parties to dominate, voters increasingly identify with groups that share their view on whether and how Britain should leave the EU.

This is dangerous territory for leaders who seek to unify, or obfuscate. Prime Minister Theresa May sought the middle ground and it swallowed her up last week. Labour leader Jeremy Corbyn tried to be all things to all voters. He, too, is facing serious questions. The opposition party has now performed abysmally in two elections in which it would be expected to do well.

However fragmenting the result of the European Parliamentary election was, the fact is that national elections aren’t decided by proportional representation but by a first-past-the-post system that accords undeniable advantage to the largest parties. Even so, the European parliamentary election poses a central question to Conservatives and Labour: What Brexit, if any, do they want?

For the Tories, it is likely that members will see May’s failures (to which a dire 9 percent showing in these elections must be added) and the Brexit Party’s success as proof they need to make a quick exit from the EU.

That increases the chances the party’s new leader will support leaving without a deal if that is the only way to exit by Oct. 31, when the current extension period ends.

Such a position would be a risky one for the un-elected head of a minority government to take — especially given that more than 9 million people just voted against a no-deal exit compared with 5.8 million for it, and that the democratically elected Parliament has sought to legislate to avoid a no-deal exit. It is likely to end in parliamentary stalemate and a general election.

Labour’s solution to its poor showing in both the recent council elections and the European vote might be to support a so-called confirmatory referendum that pits remaining in the EU with a specific leave option. Only which one? So far, Parliament cannot agree on any leave option, having rejected May’s deal.

Putting a no-deal Brexit before voters might seem a way through. But that is hardly more specific than the original leave option, since the U.K. will then need to have some kind of trading relationship with the EU, its largest and closest partner, and that will be subject to negotiations. For all the talk of trading on World Trade Organization terms, it is merely a lowest common denominator on which countries build their commercial relationships.

Even to start those negotiations will require assurances on keeping the Irish border open as well as agreement on other divorce terms, the EU has made clear. So no deal is simply another way of saying all the same questions must be decided after Oct. 31 — only without the safety net of the transition period May’s deal provided.

The advantage of so stark a choice is that a no-deal exit may scare enough people to tip the balance toward remain. The risk is that it has been so normalized by the Brexit Party (and indeed May’s “no deal is better than a bad deal” mantra) that many will say simply “bring it on.” Could the leader of the Conservatives, a party that has long defended the interests of consumers, shopkeepers and the wider economy, take that risk?

And what will the Conservatives do about Farage stealing their supporters? Two-thirds of the Brexit Party’s support came from Tory voters, according to Lord Ashcroft Polls. Many of his audiences during the campaign were a mix of traditional Conservative voters, who prefer lower taxes and smaller government, and working class Labour voters who favor more redistributionist policies. Farage will try to duck the hard questions and focus on his key themes of betrayal and trust, but it won’t be so easy now that he wants to build a party that can contest a general election.

Farage himself responded furiously to the suggestion that his first-place finish was really second best. “If you look across the country it’s about 52:48 — we’re pretty much where we were three years ago,” he told ITV’s Good Morning Britain on Monday. “Things haven’t changed, people haven’t changed their minds.”

Only a new referendum would establish whether that’s true; most polls now put remain ahead. But the European elections confirmed what has been evident to anyone watching the slow-motion train wreck in Parliament over the past nearly three years: Positions on both sides of the debate have ossified.

Britain’s two-party system has been stretched to the breaking point. And yet none of the smaller parties are likely to be able to form a governing majority under current electoral rules. It’s still the big-tent parties who must respond to the challenge laid down by voters last week, or else break up so that other groupings can gain critical mass. There is little chance of either happening without a further vote — be it a general election or another referendum.

Therese Raphael writes editorials on European politics and economics for Bloomberg.

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