As recently as last week, Mrs. May’s office said she had no plan to meet separately with them to address the issue.
But she reversed course and on Tuesday, she met with 12 Caribbean Commonwealth leaders, and apologized. “We are genuinely sorry for any anxiety that has been caused,” she said.
Until last week, the Home Office, the agency that administers immigration policy, had advised Caribbean-born residents to hire lawyers, which many of them cannot afford. This week, the Home Office dropped that stance, announcing a dedicated team to help people sort out their immigration status free of charge, and promising resolutions in two weeks, rather than the months it has taken in the past.
The prime minister’s office even suggested that the government might reimburse people for expenses incurred during their struggles to secure legal status. But no one knows the scope of the problem.
Neither the government nor its critics know how many people belong to the “Windrush generation,” those who migrated legally from British colonies or former colonies between 1948 and 1973. They do not know how many are unable to prove that they are in the country legally, how many have faced dire consequences as a result or whether any have been wrongly deported.
The stories of mistreatment began with left-leaning publications, but spread to right-leaning news media outlets. The Times of London, usually friendly to the Conservative Party, editorialized on Tuesday that the prime minister’s policies suffered from “the corrosive assumption that immigrants are a problem rather than a benefit.”
On Monday, Amber Rudd, the home secretary, endured a torrent of abuse in the House of Commons. “Some of the way they have been treated has been wrong, has been appalling, and I am sorry,” Ms. Rudd said.
The most emotional statement came from David Lammy, a Labour member of Parliament whose parents immigrated to Britain from Guyana.
“It is inhumane and cruel for so many of that Windrush generation to have suffered so long in this condition,” Mr. Lammy said. “This is a day of national shame.”
He and other opposition lawmakers demanded that Ms. Rudd say how many people had been wrongly deported to Caribbean countries they barely remembered from childhood. She insisted that as far as she knew, none had been.
Unlike most European countries, Britain does not have a national identity card, and many people do not have passports, which require proving one’s identity and residence. Until recent years, routine aspects of British life required little documentation.
That changed in 2012, when the government sharply tightened immigration controls, requiring people to prove their identity and legal status in the country in order to get a job, rent an apartment, receive free medical care, open a bank account or enroll in school, among other things. Enforcement of those rules increased in the ensuing years.
The politician most closely associated with those policies is Mrs. May, who instituted them when she was home secretary.
“The aim is to create, here in Britain, a really hostile environment for illegal immigrants,” she said in 2012.
Her opponents frequently throw that line back at her, charging that she has applied a “hostile environment” policy to all immigration, legal or illegal.
More than two million citizens of other European Union countries are believed to live in Britain, thanks to European Union rules that ease movement across borders. That fact spurred many people to vote for Britain’s exit from the European Union in a 2016 referendum, and Conservative lawmakers have promised new migration controls once Britain leaves the bloc.
Mrs. May has said that European Union citizens already in Britain will not be deported, but many of them, mistrustful of the government and wary of the anti-immigrant mood, have already left or are contemplating leaving.
The Windrush generation dates to 1948, when British law granted a form of citizenship to people from the colonies. They were encouraged to move to Britain to fill a labor shortage and could migrate without any immigration controls.
The first large group from the West Indies, almost 500 people, arrived that year on the Empire Windrush, a passenger liner, and the name stuck to an entire generation.
In 1962, British law changed to end the automatic right of entry. During the 1960s and 1970s, as the Caribbean colonies gained independence — giving their people different citizenship — a series of British laws further tightened immigration controls.
One of those laws provided that anyone from a former colony who resided legally in Britain before Jan. 1, 1973, could remain indefinitely. More than half a million people, primarily from the Caribbean, fall into that category, and most eventually acquired British citizenship, according to the Migration Observatory at the University of Oxford.
According to a government survey, more than 50,000 of those people say they are not British citizens, “but it’s hard to know what that means, really,” said Madeleine Sumption, director of the observatory. “You have people who believe that they are U.K. nationals and don’t realize that they are not. But there are also people who may in fact be U.K. citizens but don’t know.”
People who moved to Britain from 1948 to 1962, when migration was unrestricted, might not have any documentation of their arrival or their residence before 1973. Many believe they are full-fledged British citizens; experts say their status is not completely clear, though their legal right to live in Britain is undisputed.
Adults who migrated from 1962 to 1972 received documentation when they arrived, but still might not have anything proving residence before 1973. And if they brought children with them, those children — now in middle age or older — might not have ever had any immigration or other paperwork in their own names.
Ms. Rudd vowed in Parliament that the government would help people find documentary evidence of their legal status.
But Chuka Umunna, a Labour lawmaker, asked a question for which no one had a ready answer: “What if the evidence doesn’t exist?”