A man in Berlin holds up the German newspaper Bild with the headline "OUTsch!" (Axel Schmidt/Reuters)

The vote in Britain to leave the European Union lays bare the most dangerous obstacle confronting the world’s most ambitious economic and political bloc: the voice of the European people.

The elites who forged the union — a sprawling labor and consumer market of more than 500 million people — have for decades pursued an agenda of deepening integration. French bakers, German bankers and Italian restaurateurs would find themselves beholden to Brussels — the administrative capital now viewed with the same amount of voter sympathy in the towns and villages of Europe as Washington in the American heartland.

The British result amounted to a shock because of its sweep — an outright pullout from the E.U. It forces Europe to face the fact of broad public discontent with the E.U., by no means confined to Britain. Voters in France, Ireland and the Netherlands have previously made that clear when refusing to endorse various proposals that would have furthered European integration. But the United Kingdom’s vote was a direct challenge to the E.U.’s viability.

And alarmed leaders fear a domino effect of exit votes that could unravel the bloc. They are vowing a swift reinvention of a cumbersome, complicated and often confusing institution that the average European loves to hate.

Even those who support the E.U’s lofty ideals concede a profound disconnect between the bureaucrats in Brussels calling for “more Europe” — a slogan meaning more integration — and the millions of citizens they serve who say they want less.

In a stunning victory for the "Leave" campaign, Britain has voted to exit the European Union. Here's what happens next. (Jason Aldag,Adam Taylor/The Washington Post)

“A jolt is necessary,” French President François Hollande, who lands in Berlin on Monday for crisis talks with German Chancellor Angela Merkel and Italian Prime Minister Matteo Renzi, said after the British referendum. He added, “The E.U. must be understood and controlled by its citizens. I will do everything to secure profound change rather than decline.”

‘I understand the British’

On the streets of south Berlin, in the lower-middle-class neighborhood of Rudow, bakeries hawk pretzels and strudels as drivers — prompted by an ongoing European soccer tournament — cruise by in cars adorned with German flags. In a district much changed by the force of E.U. labor laws, the black, red and yellow of Team Germany are competing with the red and white banners of more recent arrivals from Poland.

In this corner of the progressive German capital, more and more voters support the Alternative for Germany party, a populist movement that recently published a manifesto calling for the dissolution of the E.U. Ralf Gotthardt, a 58-year-old retired bus driver smoking a cigarette in front of the local supermarket, offered a picture of the resentment threatening the bloc.

“I understand the British,” he said. “Decisions are just being made over our heads, and we need a referendum. The English did the right thing.”

He blames the E.U. for just about everything subpar in Rudow. For the non-German-made washing machines in local stores that “break after only two years.” For goods and services that seem to cost more than they used to. For the E.U.’s failure to come up with a real plan for handling a record wave of migrants from the Middle East. For crime — which he sees as the byproduct of the free flow of movement across European borders.

Even before the British vote, a poll by the Pew Research Center suggested the extent of the citizen backlash. The populations, if not the governments, in Eastern European nations such as Poland and Hungary are the bloc’s strongest supporters. But the French, the poll showed, actually dislike the E.U. more than the British. And a majority of Greeks and pluralities of Swedes, Dutch, Germans, Italians and French said they wanted some E.U. powers returned to their national governments.

For generations, the continent’s citizens saw the push for European integration — born of the ashes of World War II — as a bulwark against more violence.

The fall of the Soviet Union was celebrated as a triumph for grand Western projects such as the one in Brussels. So leaders pushed forward with even tighter integration, sweeping away internal borders, then embracing the common euro currency, which made it possible to save money in one nation and spend in another.

But leaders were reluctant to hand over the real political power to Brussels, leading to the debt and migration crises still dogging Europe today.

When voters in France and the Netherlands rejected a proposed E.U. constitution in 2005, E.U. leaders came back two years later and implemented many of the same changes through a different legal path that did not require voter approval. That helped fuel a sense that the E.U.’s expanding ambition had a life of its own, unchecked by national will.

Also unchecked, critics say, are E.U. rules. Bakers in Scandinavia rebelled in 2013 when the E.U. tried to limit the amount of cinnamon in baked goods to 15 milligrams per kilogram of dough, after studies found that excessive consumption of a chemical found in the spice caused liver damage. British voters loved to mock regulations about “bendy bananas,” a requirement that bananas be “free from malformation or abnormal curvature.”

“We must ask the question of whether so many decisions need to be taken in Brussels,” said Günter Verheugen, a former E.U. commissioner from Germany. “It’s simply too much. I don’t think this is what the people of Europe want.”

Byzantine bureaucracy

In Brussels, at an exhibition at the granite-and-steel European Parliament building devoted to explaining the E.U.’s byzantine workings to the public, visitors on Saturday traced the arc of E.U. history in a long hallway. Each of the 28 member states had its own section.

One large group of visitors to the center, known as the Parlamentarium, were students getting master’s degrees in European studies — essentially a graduate program in how the E.U. works. Many aspired to working inside the bloc’s institutions and were devoting more than a year to studying the intricate patchwork of commissions, directorates, councils and Parliament.

It is, perhaps, telling that a higher degree is needed to fully grasp the E.U. — a fact that has isolated it from many of the citizens it serves.

“I think it would be better if people understood how the European Union worked, because then they could understand what it’s actually doing,” said Nathalie Nied, 24, a graduate student from Germany in the program that is taught in French, German and English.

Inside Brussels’ corridors of power, there is a furious argument underway about how to respond to the British vote. Some leaders say that the rejection should inspire a wholesale rethinking of how the E.U. relates to its citizens and perhaps a permanent trimming of its ambitions. But others say that the best course is to keep doing what they have always done: to push forward with integration and pooled sovereignty, in the faith that a perfected project will prove its worth to ordinary voters.

“There’s this anti-elite thing, populist movements, facts do not count,” said Elmar Brok, a German who has been a member of the European Parliament since 1980. “You have to do what is needed; do not be afraid of the populists. You have to prove that their accusations are wrong.”

Birnbaum reported from Brussels. Stephanie Kirchner in Berlin contributed to this report.