Eighteen members of the UK's Windrush generation who could have been wrongfully removed or detained are to get a formal apology.
Home Secretary Sajid Javid said a review of 11,800 cases had identified the 18 as those "most likely to have suffered detriment because their right to be in the UK was not recognised".
He will also direct them to a compensation scheme being set up.
Any who have left the UK will also be helped to return, Mr Javid said.
The Windrush generation refers to those who moved to the UK from Caribbean countries between 1948 and 1971 but were not given proper documentation proving their indefinite right to remain.
They said the lack of documentation had posed numerous problems, for example getting jobs, accessing healthcare or even remaining in the UK.
In addition to the 18 cases, officials have identified 146 other cases of people of Caribbean Commonwealth nationality, born before 1973, who were detained or deported.
Mr Javid says the way the 164 individuals were treated and the "degree of detriment" varies considerably.
In a letter to the Home Affairs Committee, Mr Javid has also given updated figures on the number of Windrush migrants whose status in the UK has been confirmed following the establishment of a taskforce in April.
A total of 2,272 have received documents confirming their right to be in the UK, out of 6,507 people who had contacted a helpline and been referred for a call back.
Of the 2,272, 1,093 are from Jamaica.
M Javid said: "The experiences faced by some members of the Windrush generation are completely unacceptable and I am committed to righting the wrongs of the past.
"I would like to personally apologise to those identified in our review and am committed to providing them with the support and compensation they deserve.
"We must do everything we can to ensure that nothing like this happens again – which is why I have asked an independent adviser to look at what lessons we can learn from Windrush."
Labour MP David Lammy, whose parents were Windrush arrivals, said the 18 were a "drop in the ocean", adding: "The apology is crocodile tears and an insult to people still not given hardship fund, left jobless, homeless and unable to afford food."
Those affected are named after the MV Empire Windrush, the ship which arrived at Tilbury Docks, Essex, on 22 June 1948, bringing workers from Jamaica, Trinidad and Tobago and other islands, as a response to post-war labour shortages in the UK.
Many stayed in the UK for decades, setting up homes and starting families but 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 Windrush arrivals to prove they are in the UK legally.