On Thursday, Britain will vote in a referendum on whether it should exit — hence, Brexit — the European Union. If it does leave, one reason will be because the British people are fed up with uncontrolled immigration. This is a story about the arrogance of Britain’s elite, with a lesson for politicians in all countries.

First, a word about the EU: If you’re in it, you can’t truly govern yourself. You don’t make a lot of your own rules, and you don’t fully control your borders. So the referendum is about much more than immigration. It’s ultimately about democracy.

But immigration is one of the most potent issues for Brexit’s backers. Over the past weeks, as they’ve emphasized it, the polls have swung in their favor, though it’s still too close to call.

Immigration’s a big deal in Britain for three reasons. First, every immigrant takes up a hospital bed or a place in a school that is paid for by taxpayers, and takes it away from a Brit. Second, while British unemployment is low, workers fear that allowing millions of immigrants into Britain has been bad for their wages. For the elite, it’s all gain: They get foreign nannies.

I’ll be blunt about the third reason: British governments of all parties have spent the past two decades lying about their policies, repeatedly promising to bring immigration down, and repeatedly doing no such thing.

From 1997, the Labour Party was in charge. It presided over regular immigration scandals, ranging from a broken asylum system to waves of migration from Eastern Europe. At the time, this appeared to be a case of systemic incompetence.

But in 2009, Labour’s immigration speechwriter spilled the beans. As he proudly wrote, “the deliberate policy . . . was to open up the UK to mass migration.” Why? Because “mass immigration was the way the Government was going to make the UK truly multicultural.”

Why did they lie about it? Because this “wasn’t . . . a debate they wanted to have in working men’s clubs.” Labour had to deceive its own core voters, as well as the nation.

After 2010, the Conservatives led a coalition government. Before that election, current Prime Minister David Cameron promised to reduce net immigration to the “tens of thousands,” a pledge that, surely by coincidence, he repeated before he won the 2015 election.

It’s difficult to believe Cameron, who opposes Brexit, thought it was possible. He must have recognized that, since all EU citizens have the right to move to the UK, Britain can’t control immigration as long as it’s in the EU. His promise was a mistake or another deception.

Either way, the results are in. In late May, the government was forced to admit that net immigration in 2015 was only a few thousand off its all-time high, at more than 330,000 a year.

I don’t believe that all this immigration is bad. Britain attracts immigrants partly because it’s got a dynamic economy. Would Britain be better off if people wanted to avoid it? But I don’t believe in open borders or enforced multiculturalism. And I don’t like dishonest politicians.

Immigration would be less controversial in Britain if it didn’t seem like a back-scratching deal between politicians and big business, a deal based on cheap nannies, cheap workers, and elite distaste for the people in those workingmen’s clubs.

All those people, though, have a vote. And while most politicians and big businesses love the EU, they’ve given lots of Britons a reason to vote to leave it. In a democracy, if you persist in giving people what they don’t want, there will be consequences. Mass immigration was meant to transform Britain. Ironically, if it gives Brexit the winning edge on Thursday, that’s exactly what it will do.