Theresa May will hold a meeting with other Commonwealth leaders to “discuss concerns” over the Windrush generation facing deportation from the UK.
Downing Street confirmed the meeting amid growing calls for the prime minister to take action.
Many long-term immigrants who arrived from the Commonwealth as children have been told they are here illegally.
Labour MP David Lammy said the meeting was a “small u-turn”, adding that he would not rest until it was sorted.
A cross-party group of more than 100 MPs had signed a letter to Mrs May asking for urgent action.
Mrs May’s spokesman said the prime minister was clear that “no-one with the right to be here will be made to leave”.
He added that the PM is “aware that many people are unlikely to have documents that are over 40 years old”.
Commonwealth leaders are in London this week for the Commonwealth heads of government meeting (Chogm).
Thousands of people arrived in the UK as children in the first wave of Commonwealth immigration 70 years ago.
They are known as the Windrush generation – a reference to the ship, the Empire Windrush, which brought workers from the West Indies to Britain in 1948.
Under the 1971 Immigration Act, all Commonwealth citizens already living in the UK were given indefinite leave to remain – but the right to free movement between Commonwealth nations was ended from that date onwards.
However, the Home Office did not keep a record of those granted leave to remain or issue any paperwork confirming it, meaning it is difficult for the individuals to now prove they are in the UK legally.
Penny Mordaunt, the international development secretary, said the government must do a better job in dealing with the immigration cases involving the Windrush generation.
She said she wanted to reassure those affected after claims that some were facing deportation and being denied access to healthcare over UK paperwork issues.
She told BBC Radio 4’s Today programme: “People who are in that situation, there is absolutely no question of their right to remain, and their right to gain access to services such as healthcare.”
Communities Secretary Sajid Javid said he was “deeply concerned” about the difficulties some of the Windrush generation were facing and the government was looking into it urgently.
A letter to the prime minister, co-ordinated by Labour’s David Lammy, called for a “swift resolution of this growing crisis”.
It said: “We urge you to guarantee the status of all Commonwealth nationals whose right to remain is protected by law and to provide an effective, humane route to the clarification of their status.”
It was signed by 140 MPs including Labour leader Jeremy Corbyn and Conservative MP Sarah Wollaston.
‘Not welcome’ in UK
Omar Khan, from the Runnymede Trust charity which has been involved in trying to tackle this issue, said the onus should be on the Home Office to help people find the documents they need.
He also called for an extension of legal aid to these cases.
He told the BBC’s Victoria Derbyshire programme: “These are individuals who do have legal rights – this is not really an amnesty. The issue is their ability to prove it through documentation is now quite difficult.”
Guy Hewitt, Barbados high commissioner, told the BBC: “I have held as a great honour the fact that I am the first London-born high commissioner for Barbados.
“This is the first time I have felt that the country of my birth is saying to people of my region ‘you are no longer welcome’.”
The Migration Observatory at Oxford University estimates there are 500,000 people resident in the UK who were born in a Commonwealth country and arrived before 1971.
People born in Jamaica and other Caribbean countries are thought to be more affected than those from other Commonwealth nations, as they were more likely to arrive on their parent’s passports without their own ID documents.
Many have never applied for a passport in their own name or had their immigration status formalised, as they regarded themselves as British.
The Guardian newspaper has highlighted a number of cases of such people being threatened with deportation.
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