Officials are investigating dozens of new migration cases relating to the Windrush generation amid mounting criticism of the government.
The Home Office said it was looking at 49 cases as a result of calls over the course of Tuesday.
Earlier Theresa May apologised over the deportation threats to children of Commonwealth citizens.
It has also emerged that landing cards belonging to Windrush migrants were destroyed by the Home Office in 2010.
Labour said this was "truly shocking", accusing the Home Office – which was run at that time by Theresa May – of getting rid of "the very records that could have demonstrated their right to remain".
But the government said such a suggestion would be "misleading and inaccurate".
The row has focused on the so-called Windrush generation, who arrived in the UK as children in the first wave of Commonwealth immigration 70 years ago, often on their parents' passports.
Changes to migration rules mean those who lack documents are now being told they need evidence to continue working, access key services or even remain in the UK.
A former Home Office employee has told The Guardian that thousands of landing card slips recording Windrush immigrants' arrival dates in the UK were destroyed in 2010 during an office move.
The former worker, who is not named by the newspaper, said managers were warned by staff that destroying the cards would make it harder to check the records of older Caribbean-born residents experiencing difficulties proving their right to remain in the UK.
Labour said it was a "fiasco" and that culpability "rests solely with the Home Office".
Shadow home secretary Diane Abbott said: "The Windrush generation have been threatened with deportation because they cannot provide documents, but now we learn that the Home Office destroyed the very records that could have demonstrated their right to remain."
The government said the decision to "dispose of" the cards had been an "operational" one, taken by officials at the UK Border Agency, rather than then Home Secretary Mrs May.
A Home Office spokesman said: "Registration slips provided details of an individual's date of entry, they did not provide any reliable evidence relating to ongoing residence in the UK or their immigration status.
"So it would be misleading and inaccurate to suggest that registration slips would therefore have a bearing on immigration cases whereby Commonwealth citizens are proving residency in the UK."
Under the 1971 Immigration Act, all Commonwealth citizens already living in the UK were given indefinite leave to remain.
However, 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 the individuals to now prove they are in the UK legally.
Changes to immigration law in 2012, which require people to have documentation to work, rent a property or access benefits, including healthcare, have highlighted the issue and left people fearful about their status.
In an apology to Caribbean leaders, Theresa May said she wanted to "dispel any impression that my government is in some sense clamping down on Commonwealth citizens, particularly those from the Caribbean who have built a life here".
She said the current controversy had arisen because of new rules, introduced by her as home secretary, designed to make sure only those with the right to remain in the UK could access the welfare system and the NHS.
"This has resulted in some people, through no fault of their own, now needing to be able to evidence their immigration status," she told the foreign ministers and leaders of 12 Caribbean nations in Downing Street.
"And the overwhelming majority of the Windrush generation do have the documents that they need, but we are working hard to help those who do not."
A new taskforce and helpline has been established for people affected.