The payments – which No 10 says will go further than the simple reimbursement of costs incurred – will “resolve the anxiety and problems” they have suffered, the prime minister said.
More than 280 people have so far contacted a Home Office helpline for members of the Windrush generation with concerns about their migration status, prompting speculation the bill could run to millions.
Closing the Commonwealth summit, Ms May acknowledged the scandal that has overshadowed the event – caused by her own tough immigration rules, critics say.
Referring to her meetings with fellow Commonwealth leaders, she said: “I gave an absolute commitment that the United Kingdom government would do whatever it takes – including, where appropriate, payment of compensation – to resolve the anxiety and problems which some of the Windrush generation have suffered.
“These people are British, they are part of us they helped to build Britain and we are all the stronger for their contributions.”
The row began when it emerged that some Windrush immigrants – who moved to the UK between 1940s to 1970s – had lost their jobs, been refused medical care or been threatened with deportation as they did not have the right documentation.
Downing Street said the payments would go beyond “reimbursement of any legal fees” run up in trying to prove a right to remain in the UK to recognise the pain inflicted by the debacle. Further details will be announced next week.
It means the prime minister’s comments go further than her apology in the Commons on Wednesday, in which she said only: “There will be no cost to them; nobody will be out of pocket as a result.”
The Grenadian prime minister, Keith Mitchell, called for “serious compensation” for people affected and said there was “no question” that Ms May should do more to help.
Speaking to reporters afterwards, he said: “Clearly it’s something which is vibrating strongly in the Caribbean region as a whole.
“Many of our people came here and helped to build Britain, under conditions that were set for them. For me, it’s very unfair for them to be treated in the way they have been treated.
“The word compensation came out today – that was highly significant, extremely important. It’s not just, ‘I’m sorry.’
“People lost a lot, people suffered a lot of pain, and they must be given an opportunity to correct this – some serious compensation.
“If not the person, if they’ve gone, then the families who have suffered too.”
Ms May’s pledge, at the close of the Commonwealth Heads of Government Meeting, came after more examples emerged of long-standing UK residents barred from returning to the country.
Gretel Gocan, 81, told Channel 5 she had been stuck in Jamaica since 2010, unable to return to her south London home after taking a holiday to visit family.
Former NHS nurse Icilda Williams, who moved back to Jamaica in 1996 after 34 years in Bradford, said her annual visits to the UK to see her children had been halted since 2014 after she was denied a visa.
Jeremy Corbyn demanded Ms May go further by apologising for the “hostile environment” policy she introduced, requiring suspected illegal immigrants to prove their right to be in the UK before receiving services.
“She’s the one that ordered the vans to go around telling immigrants to go home,” said Mr Corbyn. “She’s the one that created that nasty atmosphere.
“What’s happening is something quite disgusting. People that have given their lives to this country, to our health service, to our education system, our transport system are suddenly being told to go home.”
Mr Corbyn dismissed claims from Ms May’s former adviser, Nick Timothy, that the then home secretary had opposed the deployment of vans telling illegal immigrants to “go home”, which he said was imposed when she was away on holiday.
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