In last week’s elections for the European Parliament, British voters punished the major parties. Both the Conservatives and Labour lost votes and seats. The smaller parties, the Liberal Democrats and the Greens, enjoyed sizable gains, while the new Brexit Party, formed only months earlier by Nigel Farage for the sole purpose of getting the United Kingdom firmly out of the European Union, claimed almost one-third of the vote.

What happens when a country deeply divided about the desirability of E.U. membership votes to send representatives to the European Parliament? To answer this question, we polled a national sample of 2,525 British voters in a survey conducted by Deltapoll in the three days before the election. Here’s what we learned.

Yes, Brexit was the dominant issue

Since the 2016 referendum, Brexit has been the dominant issue in U.K. politics. The recent election took place after repeated, unsuccessful attempts by Conservative Prime Minister Theresa May to get the U.K. Parliament to pass a final Brexit deal. Unsurprisingly, over 40 percent of our survey respondents cited Brexit as the “most important” issue facing the country. Fewer than 10 percent of respondents mentioned any other issue.

Both those who want to leave the E.U. and those who want to remain are unhappy with how the government has handled Brexit negotiations. Only 9 percent said it had done well and over 70 percent said it had done badly. Three-quarters of those surveyed were unhappy with May’s performance and nearly as many said the government’s record was unsatisfactory. Less than 15 percent thought the Conservatives were the best party on Brexit or other issues.

There wasn’t much more enthusiasm about the Labour Party either. Less than 20 percent thought a Labour government would perform well, and people had more negative feelings on average about Labour leader Jeremy Corbyn than any of the other party leaders.

These attitudes help explain why the Conservatives lost over 1,300 seats in the 2019 local elections, held earlier in May. Labour fared better than the Conservatives in these contests, but still lost 84 seats — while the Liberal Democrats and the Greens gained 704 and 194 seats, respectively. Commentators concluded that the two major U.K. parties would take a “good kicking” in the E.U. election. They were right.

The Brexit Party came out of nowhere. But anti-Brexit parties did well, too.

The figure above documents the spectacular success of the new Brexit Party, which received 31.6 percent of the vote in the 2019 E.U. election. But smaller pro-Remain parties also did well. The Liberal Democrats claimed 20.3 percent of the vote, up from 6.6 percent in 2014, while support for the Green Party rose from 6.9 to 12.1 percent.

In sharp contrast, Labour’s vote share dropped from 24.4 percent to just 14.1 percent, while the Conservatives fell from 23.1 percent to 9.1 percent — their worst performance ever in a national election. Under intense pressure from her own party, May resigned before the results were announced.

The election outcome wasn’t just about Brexit. There is reason to suspect that Farage’s outsized personality helped explain the rapid rise of the Brexit Party, which was too new to have a base of steady supporters, and only had one issue — Brexit.

If we use statistical modeling that controls for several factors that might affect voting, we see that there was a predictably strong relationship between attitudes to E.U. membership and support for the Brexit party. However, there was also a strong relationship between attitudes to Farage and the probability of voting for his party. People who really disliked Farage had only a 5 percent likelihood of voting for the Brexit party, while those who really liked him had fully a 78 percent chance of doing so.

What’s next? It’s hard to tell.

Some commentators argue that public opinion has swung in a pro-Remain direction, calculating that combined support for pro-E. U. parties in the election was substantially greater than that for the Brexit party, the Conservatives and UKIP. That may be a stretch. Only 37 percent turned out to vote, which means the preferences of the large majority who failed to do so remain unknown.

And our survey reveals that not all of those voting for any of the parties were unanimously in favor or opposed to Brexit. When asked directly, 44 percent favored continued E.U. membership and 44 percent wanted to get out. And, when queried about how they would vote if a second referendum was held, Remainers and Leavers were just as balanced, both at 46 percent. As detailed in “Brexit — Why Britain Voted to Leave the European Union,” a book co-written by two of us, opinion polls showed that the distribution of pro- and anti-E. U. sentiment was extremely close at the time of the 2016 referendum. What we just learned is that this remains true today — the Brexit battle continues.

Again, Brexit is not all that is at stake, even in the European Parliament elections. The Conservatives and Labour have dominated U.K. politics for generations — but there are signs that public discontent may be eroding their support. For instance, a survey question that asked how respondents would vote in the next general election revealed only 30 percent would support Labour and even fewer would vote Conservative.

If British voters behaved in this fashion in the next election, neither major party could form a majority government. Coalition governments and a genuine multiparty system may be the future of British politics.

Harold Clarke teaches at the school of economic, political and policy sciences at the University of Texas at Dallas.

Marianne Stewart teaches at the school of economic, political and policy sciences at the University of Texas at Dallas.

Paul Whiteley teaches in the government department at the University of Essex.