“I want to apologise to you today. Because we are genuinely sorry for any anxiety that has been caused,” she told the hastily-convened gathering.

She added: “I want to dispel any impression that my government is in some sense clamping down on Commonwealth citizens, particularly those from the Caribbean.”

The government has faced outrage for its treatment of people who came to Britain between 1948, when the ship Windrush brought over the first group of West Indian immigrants, and the early 1970s.

They and their parents were invited to help rebuild Britain after World War II and with many of them legally British — they were born while their home countries were still colonies — they were given indefinite leave to remain.

But those who failed to get their papers in order are now being treated as illegal, which limits their access to work and healthcare and puts them at risk of deportation if they cannot provide evidence of their life in Britain.

The row, which one MP called a “national shame”, has been hugely embarrassing for the government as it coincides with this week’s meeting of the 53 Commonwealth heads of government in London.

‘Make good any injustice’
Timothy Harris, prime minister of Saint Kitts and Nevis, expressed hope that Britain would “do the right thing and make good any injustice,” including through compensation.

Jamaican Prime Minister Andrew Holness, who earlier had a bilateral meeting with May, said he wanted a “speedy” response.

The now elderly people involved “have significantly contributed to the building and enrichment of the country”, he said.

“Now these persons are not able to claim their place as citizens.”

Britain has written to each of the Caribbean governments setting out how it intends to rectify the situation, notably by helping anyone affected to find the necessary paperwork to regularise their immigration status.

It has promised to waive the usual fee for residency cards, and “reimburse reasonable legal costs” incurred so far.

Holness said to May in their talks: “Prime minister, we welcome your response and we look forward to a speedy implementation of your proposed solution.

“It will lead to security, certainly for those who have been affected… It is time for the inclusive prosperity for which we stand as Commonwealth people.”

Antigua and Barbuda Prime Minister Gaston Browne earlier said an apology from May “would be welcome” but he was “pleased” the government had stepped in.

“Many of these individuals do not have any connection with the country of their birth, would have lived in the UK their entire lives and worked very hard towards the advancement of the UK,” he said.

Questions over EU citizens
The issue has come to light following a clampdown on illegal immigration in recent years, with requirements for people to have documentation to work, rent a property or access benefits including healthcare.

But it has sparked concern about London’s ability to deal with millions of European citizens currently living in Britain who want to stay after Britain leaves the European Union next year.

Ministers have agreed they will be given indefinite leave to remain, but they must apply for a new status.

Guy Verhofstadt, the European Parliament’s Brexit coordinator, was quoted by The Independent as saying: “This will be deeply worrying for millions of EU citizens in the UK who will now fear similar treatment after Brexit.”

A spokesman for May’s office said: “Work has been going on for some time now in creating a system to handle those claims.

“We’re confident that we will be able to do it in a smooth and efficient way.”