Prime Minister Theresa May is under pressure to resolve the status of thousands of British residents who arrived from the Caribbean decades ago and are now being denied basic rights after being incorrectly identified as illegal immigrants.
Dave Prentis cited the case of Albert Thompson, who has lived in the United Kingdom for 44 years, who has been told he has to pay £54,000 to have treatment for prostate cancer.
Home Secretary Amber Rudd told MPs this afternoon that she had set up a new Home Office taskforce "to ensure a swift response" to people's concerns about their immigration status, and said she would be waiving fees involved for those affected.
There is growing anger that long-term British residents have fallen victim to rule changes in 2012 aimed at stopping overstaying. Children could come in on their parents' passports.
PoliticsHome asked the Home Office to clarify whether any citizens have been deported in error, and whether the department was aiming to directly contact them if so.
The row has threatened to overshadow Britain's hosting of the annual Commonwealth Heads of Government meeting in London this week.
Mr Lammy said: "When my parents and their generation arrived in this country under the Nationality Act of 1948, they arrived here as British citizens".More news: France's Macron: 'Cannot Tolerate Use of Chemical Weapons'
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Thousands of Windrush migrants who arrived in the United Kingdom after World War Two are being threatened with deportation amid rule changes.
Nearly half a million people left their homes in the West Indies to live in Britain between 1948 and 1970, according to Britain's National Archives.
The Home Secretary said high commissioners would have an opportunity to raise any such cases with her at their meeting later this week.
"The impact has been felt in the cases of individuals losing the right to work, to rent property, to receive pensions, to access their bank accounts or even to access vital healthcare - a particularly cruel twist of fate as so many of those affected have spent their lives in the service of our National Health Service".
On Friday, the Home Office issued guidance admitting that problems were coming to the fore because of newly tightened immigration rules, noting: "Recent changes to the law mean that if you wish to work, rent property or have access to benefits and services in the United Kingdom then you will need documents to demonstrate your right to be in the UK".
An online petition calling for an amnesty for those who arrived in Britain from Commonwealth countries in the Caribbean as children, and a lowering of the level of documentary proof required from people who have lived here since they were children, has now attracted more than 136,000 signatures.
Mrs May's official spokesman said: "She deeply values the contribution made by these and all Commonwealth citizens who have made a life in the United Kingdom, and is making sure the Home Office is offering the correct solution for individual situations".