Theresa May is to meet Caribbean leaders after ministers apologised for the Government's "appalling" treatment of the so-called Windrush generation.
Home Secretary Amber Rudd announced on Monday she was setting up a new taskforce to speed up the regularisation of the immigration status of people who arrived in the UK as long ago as the 1940s.
The move came amid growing anger that people who had lived in Britain since they were schoolchildren were now being denied access to healthcare and threatened with deportation due to UK paperwork issues.
Downing Street insisted no one with a right to be in the country would be made to leave and the Prime Minister will seek to offer further reassurances when she meets Caribbean leaders in the margins of the Commonwealth Heads of Government Meeting (Chogm) in London on Tuesday.
In the Commons on Monday, Ms Rudd acknowledged the Home Office had become "too concerned with policy and strategy" at the expense of the individual.
"I do not want any of the Commonwealth citizens who are here legally to be impacted in the way they have," she told MPs.
"Frankly, some of the ways they have been treated has been wrong, has been appalling and I am sorry."
Ms Rudd said fees for sorting out the paperwork of those affected would be waived so they could have their status confirmed free of charge.
She said she had also given instructions that there were "no removals or detention" of Commonwealth citizens under the new assistance scheme.
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 theWindrush generation.
Labour MP David Lammy who organised the letter said it was a "day of national shame" and that it was "inhumane and cruel" that so many people had had to live with such uncertainty for so long.