Margaret Thatcher predicted that it would end in tears. She described “the drive to create a European superstate” as “perhaps the greatest folly of the modern era.” The late British prime minister knew the lesson of the past: When politicians try to impose grand designs on peoples of different histories, languages and cultural allegiances, the edifice totters and collapses.

Once devoutly pro-European, Thatcher had come to worry by the late 1980s that grand projects emerging from Brussels, like the effort to create a single European currency, would centralize power and create a vast bureaucracy. She saw that democratic accountability would be impossible across a wildly polyglot European Union. And she feared that the sort of cronyism and collusion among big business and politicians that she had dismantled in the U.K. would re-emerge in Brussels. Almost every one of her fears has been vindicated.

Britain will soon have the opportunity to decide whether or not to remain a part of the European project that it joined in 1973. After EU leaders agreed late Friday to several key British demands, including a so-called emergency brake to let the U.K. restrict welfare benefits for EU migrants, a nationwide referendum is likely to be held in June, fulfilling a promise made by Prime Minister David Cameron at the last general election. Polls suggest that the outcome of the vote is too close to call, but a British exit—or “Brexit”—is a real possibility. It would also be a wise choice, for the U.K., for Europe and for the U.S.

Prominent Conservative politicians, including Iain Duncan Smith and Michael Gove, are expected to campaign for Brexit, endangering the unity of the government. But Mr. Cameron, most of his top ministers, the leader of the opposition Labour Party and the country’s largest businesses will hold firm with the EU. They will argue that Britain should not walk away but should remain at the EU’s highest table, helping to fix the continent’s problems. They worry that if Britain leaves the EU, London won’t be able to influence the rules that govern the world’s richest single market, with more than 500 million people.

In normal times, this alliance of powerful businesses and politicians would be enough to guarantee victory for the pro-EU cause. But as the U.S. presidential race continues to prove, these are not normal times, and having the establishment on your side can be more of a burden than a blessing. Donald Trump and Bernie Sanders have amplified the hunger for change of an electorate that is angry at big business, concerned about rising immigration and anxious over economic insecurity. In Britain, the EU gets much of the blame for such ills. It was the anti-EU camp, not the backers of European unity, that celebrated when Goldman Sachs recently announced its support for having the U.K. stay put.