Often they did not formally apply for British citizenship or a passport.
The British government has promised to act to reverse "terrible mistakes" made over the treatment of immigrants from the so-called "Windrush" generation, after revelations that people who came to the United Kingdom decades ago are being told to leave the country.
An online petition calling for an amnesty for those who arrived in Britain from Commonwealth countries in the Caribbean as children, and a lowering of the level of documentary proof required from people who have lived here since they were children, has now attracted more than 136,000 signatures.
"Frankly, some of the ways they have been treated has been wrong, has been appalling and I am sorry". She couldn't, however, confirm the number of people who ended up being deported following the Home Office's draconian immigration policies.
There is growing unease among politicians about the situation, which has affected an unknown number of people who arrived in the United Kingdom as children, but never formally naturalised or applied for a British passport.
Concerns have been raised following cases where people who came to the United Kingdom as children in the 1950s and 1960s were now facing immigration issues despite having lived in the United Kingdom all their adult lives.
Answering questions in the House of Commons later, Home Secretary Amber Rudd vowed to "find out if there are any such people who have been removed".
The Prime Minister will now meet with the leaders on Tuesday.
"Theresa May must apologise for this mess which has taken place as a direct effect of the hostile environment she created".
SNP home affairs spokesperson Joanna Cherry expressed hope the Home Secretary's words are a hint "she is going to review" the Government's "hostile environment" immigration policy.
Theresa May will meet representatives of 12 Caribbean countries this week to discuss the immigration problems experienced by some British residents of the Windrush generation, in an apparent U-turn on the issue.
In a tweet accompanying the article, the Home Office said Nokes "dispels the myth that this government is clamping down on Commonwealth citizens".
Barbados high commissioner to the UK, Guy Hewitt, claimed he had initially been told the Prime Minister's schedule was "full" this week.
Mrs May's official spokesman said: "She deeply values the contribution made by these and all Commonwealth citizens who have made a life in the United Kingdom, and is making sure the Home Office is offering the correct solution for individual situations".
She added: "This issue came to light because measures introduced in recent years to make sure only those with a legal right to live here can access things like NHS treatment and rented accommodation, meaning people must now be able to prove their status".
The announcement came after a cross-party group of 140 MPs wrote to Mrs May calling for an "immediate and effective" response to problems faced by members of the Windrush generation.