But Number 10 said that the PM only became aware of the request this morning and hoped to meet as many of them as possible this week, while they are in London for the Commonwealth summit.
Regulations introduced by Prime Minister Theresa May, when she was Home Secretary in the previous Conservative government led by David Cameron, require employers, landlords and health service providers to demand evidence of legal immigration status.
"We want people to have confidence to come to the Home Office, we want to give them a message of reassurance, because we value these people".
Theresa May is to meet counterparts from Caribbean states this week to discuss problems faced by long-term British residents from the Windrush generation over their immigration status, Downing Street has announced.
Some British residents, some of whom moved to the United Kingdom from the Caribbean more than 50 years ago, have been threatened with deportation, while others have lost their jobs.
Downing Street has rejected a diplomatic request to discuss the immigration challenges being faced by some Windrush-generation British residents.
The home secretary, Amber Rudd, is expected to provide more details in a statement in the Commons on Monday afternoon.
Glenda Caesar was just six months old in 1961 when she traveled from Dominica to the United Kingdom with her parents.
More than 140 lawmakers have signed a letter calling on May to resolve an anomaly that means many people who immigrated as children between 1948 and 1971 are being denied health services or prevented from working. "I am not working at present and still need documentation on my father and school or medical records as the final part".
The Tottenham MP said it was a "national shame" that it had taken so long for the government to speak on the issue, calling it "inhumane and cruel" for those who waited for them to act.
Patrick Vernon, an expert on Caribbean family history in the United Kingdom, organized a petition that received more than the 100,000 signatures required for a debate on the issue to be held in parliament.
Barbados High Commissioner Guy Hewitt told the BBC: "Because they came from colonies which were not independent, they thought they were British subjects".
"It's like telling the descendants of fourth generation Irish immigrants to the USA that suddenly you might not be American after all and could be deported", Vernon told CNN.
Intensifying the row, junior home office minister Caroline Nokes admitted today that some people may have been deported in error. This should not happen to people who have been longstanding pillars of our community.
"She is aware that many people are unlikely to have documents that are over 40 years old, and she is clear that no one with the right to be here will be made to leave", the spokesman said.
However, the Home Office did not keep a record of those granted leave to remain or issue any paperwork confirming it, meaning it is hard for the individuals to now prove they are in the United Kingdom legally.
"We will handle every case with sensitivity and will help people understand what is required and help them gather the information they need".