On June 23, Britain faces a fateful decision: whether or not to leave the European Union. And the world will be watching. (Daron Taylor,Jason Aldag,Danielle Kunitz/The Washington Post)

British Prime Minister David Cameron was only minutes into a final push to persuade his country to stay in the European Union this week when he invoked the e-word: experts.

“It’s not just the ‘remain’ side,” he said, rattling off warnings of a cataclysm to come if Britain votes to leave. “You’ve got expert after expert: the OECD, the IMF, the Bank of England, the Institute for Fiscal Studies.”

His audience of common-man interrogators on the BBC’s vaunted “Question Time” program was unmoved. The Bank of England, one elderly man dismissively told his prime minister, had been wrong three times on interest rates alone. Why should it be trusted now? And if the experts all say “stay,” a middle-aged woman asked pointedly, then why was Britain on the verge of Brexit?

When the country goes to the polls Thursday, voters will be asked a simple question: Should the country stay in the E.U. or get out?

But as much as anything, the vote is shaping up as a referendum on whether Britain still trusts the people who supposedly know the most about economics, international relations and global security. The vast majority of authorities in all three fields have said that leaving could be disastrous.

Nonetheless, with only two days to go before the country votes, polls show a tie that could swing either way.

If Britain does vote to go, it will be the culmination of a shift underway for more than a decade as the country has lost faith in those who are supposed to have the answers. The Iraq War, the global financial crisis and scandals large and small involving the high and mighty of British society have all contributed.

“What we’re seeing is a rise in the number of people who are dissatisfied, disapproving, distrusting of political institutions, political parties, the establishment, the media and, wrapped up with that, the experts,” said Joe Twyman, head of political and social research at the polling firm YouGov. “A certain proportion of people don’t believe a word of what they hear from those they consider part of the metropolitan elite.”

Of course, Twyman noted, Britain is not the only country where that’s true. The rise in the United States of Donald Trump, a man not known for his fidelity to facts and who breezily dismisses expert opinion, exemplifies the trend on the other side of the Atlantic.

But unlike elections, which can be undone with the next vote, Britain’s choice on Thursday is considered irrevocable. And it has the potential to mark the biggest change in the country’s global role since it shed its empire after World War II.

The fact that so much of the country wants to leave in spite of — or perhaps in part because of — an establishment consensus that Britain is better off staying in has challenged Britain’s notion of itself as a nation of pragmatic people who, when others veer wildly to the extremes, always make the rational choice.

Since February, the pro-E.U. camp has trotted out endorsement upon endorsement from respected authorities within Britain and beyond, including President Obama. None of it seems to have made a dent.

That’s been exasperating for “remain” leaders. Amid challenges from audience members over basic facts about the country’s E.U. membership, Cameron appeared on the verge of losing his temper when he made his case Sunday evening on “Question Time.” He said voters had become “confused” by the lies of pro-Brexit politicians and urged his countrymen to simply do what they would with any other decision.

“The ‘leave’ campaign say, ‘Let’s not listen to experts,’ ” he said. “But if we are about to get into a car and drive our children on a motorway, and a mechanic says, ‘The brakes don’t work, the petrol gauge is faulty, the steering isn’t working,’ we wouldn’t get in the car.”

The pro-Brexit advocates, Cameron argued, “are asking you to trust in just a sense it’s going to be okay, and I don’t think that’s good enough.”

But for many voters, it apparently is.

“We’ll be better off without the E.U. There’s no doubt about it. I’m not worried about nothing,” said Stephen Waller, a retired, 61-year-old “out” supporter. “That’s my opinion, obviously. Experts have their opinion. But I think we’ll be better off.”

Politicians advocating “leave” have delighted in the country’s populist, anti-expert mood, and have fed it by dismissing the views of economists, scientists, military commanders, business leaders and others as part of an elitist conspiracy, “an establishment stitch-up.”

“There is only one expert that matters,” said Gisela Stuart, a Labour member of Parliament who wants out of the E.U., “and that’s you, the voter.”

Challenged on Sky News this month to name one credible economic authority who supported an E.U. exit, leading Brexiteer Michael Gove was defiant.

“I’m glad these organizations aren’t on my side,” said the ­Oxford-educated secretary of state for justice. “I think people in this country have had enough of experts.”

He clarified his comments in remarks to the BBC on Tuesday morning, saying that independent economic forecasting firms had counseled Britain to get into the common European currency, the euro, when it was first created in 1999. Britain stayed out, and most Brits are glad it did.

“If economic forecasters were as reliable as doctors or airline pilots, then everyone would be a billionaire,” Gove said.

Indeed, the performance of economic and political experts in recent years has hardly been inspiring. Most missed signs that the global financial system was headed for a crash in 2008. Weapons of mass destruction were never found in Iraq. Even the rise of Trump and the potential for Brexit were ignored by most political cognoscenti for far too long.

The reluctance of Britons to believe the word of experts isn’t limited to “leave” voters. Surveys conducted this month by YouGov show that even majorities of “remain” voters wouldn’t trust politicians, foreign leaders, religious authorities or newspaper journalists.

But “leave” voters say they don’t really trust anyone. The difference between the two camps, Twyman said, is that “leave” voters “believe experts never get it right. If you’re a ‘remain’ voter, you believe that experts don’t always get it wrong.”

Perhaps sensing that the reliance on experts isn’t cutting through, the “remain” campaign has begun to tout the opinions of celebrities. On Tuesday, it heralded the endorsement of international soccer star David Beckham.

But Twyman said the only endorsements that would truly make a difference at this stage are two that neither side is likely to get: Prince William and Prince Harry, heirs to the throne who, like all members of the royal family, are sworn to stay out of politics. Both have broad appeal that’s weathered the anti-establishment storm because, ironically, they’re not seen as part of the establishment.

“Will and Harry are seen as ordinary people like us,” Twyman said, “who just so happen to have been ordained by God to reign over us.”

Karla Adam contributed to this report.