When Nicola Procaccini was elected to the European Parliament six years ago, colleagues seemed to avoid stepping into elevators with him at the towering glass Parliament building in Brussels, he said. He belonged to a tiny, fringe party on the right of Italian politics whose hard-line stances on immigration were scorned.

“My hand would hang midair because they don’t shake hands with fascists,” Mr. Procaccini said in an interview, derisively characterizing how he thought his opponents saw him. Meanwhile, migrant rights activists were invited into the Parliament chamber and cheered.

Now those tables have turned, he said. “Those who told us our approach was racist, xenophobic, are slowly starting to say, ‘Well, maybe they’re a bit right,’” Mr. Procaccini said, noting that mainstream politicians are now embracing more of his party’s policies on migration.

Mr. Procaccini’s party, Brothers of Italy, is now very popular in Italy. Its leader, Giorgia Meloni, is the country’s prime minister. And Mr. Procaccini is a chairman of the European Conservatives and Reformists group, a big force in the European Parliament.

Ten days ago, Britain’s prime minister, Keir Starmer, vowed to take “back control of our borders,” warning that uncontrolled immigration could result in the country “becoming an island of strangers, not a nation that walks forward together.”

On Thursday, the government estimated that net migration had dropped by almost half in 2024 compared to 2023, to 431,000, suggesting that Britain’s era of soaring immigration, far from worsening, was gradually coming to an end.

The gap between Mr. Starmer’s alarming language and the numbers underscored how rising populism, fueled in Britain by the politics of Brexit, has twisted the debate on immigration, sometimes leaving it strangely disconnected from the facts.

The sharp drop in net migration, which had been predicted, mainly reflected tighter measures on immigration put in place by the previous Conservative government, which faced acute pressure to reduce a surge that began after Brexit.