Home Secretary Amber Rudd has offered an apology in the House of Commons to members of the so-called Windrush generation who have been subjected to what she described as "appalling" treatment by the Government.
Ms Rudd announced the creation of a new task force in the Home Office to speed up the regularisation of the immigration status of people who arrived in the UK as long ago as the 1940s.
Her announcement came after Downing Street said Prime Minister Theresa May wanted to ensure that "no-one with the right to be here will be made to leave".
And Communities Secretary Sajid Javid said he was "deeply concerned" at challenges to the immigration status of people who were "long-standing pillars of our community".
Immigration minister Caroline Nokes appeared to suggest that some individuals may already have been deported in error.
But Ms Rudd told the House of Commons that she would not know whether this had happened until she meets high commissioners from Caribbean nations later this week.
Mrs May is to meet her counterparts from Caribbean states in the margins of the Commonwealth summit in London on Tuesday amid growing anger about individuals facing the threat of deportation and being denied access to healthcare due to UK paperwork issues.
Ms Rudd was challenged in the Commons over an interview in which Ms Nokes appeared to confirm that some Windrush migrants had been wrongly deported.
"There have been some horrendous situations which as a minister have appalled me," the immigration minister told ITV News in response to a question about deportations.
"I don't know the numbers, but what I am determined to do going forward is to say we will have no more of this."
The Home Secretary said high commissioners would have an opportunity to raise any such cases with her at their meeting later this week.
And she said: "I do not want any of the Commonwealth citizens who are here legally to be impacted in the way they have.
"Frankly, some of the ways they have been treated has been wrong, has been appalling and I am sorry.
"That's why I am setting up a new area in my department to ensure that we have a completely new approach to how their situation is regularised."
Ms Rudd said that fees for sorting out the paperwork of those affected would be waived so that they can have their status confirmed free of charge.
Mrs May's official spokesman said the Prime Minister "deeply values" the contribution made by Commonwealth citizens in the UK, and was "clear that no-one with the right to be here will be made to leave."
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 the Windrush generation.
The letter to the PM was co-ordinated by David Lammy, chairman of the Race and Community All Party Parliamentary Group, and has the backing of Labour leader Jeremy Corbyn and Conservative MPs such as Sarah Wollaston.
It called for action over the immigration anomalies, stating: "All too often these routine bureaucratic errors bring about the separation of families and irreparable damage to lives in addition to undue stress, anxiety and suffering.
"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."