Forty-nine new cases are being looked into after a helpline was set up for Windrush generation immigrants, the Home Office has said.
It comes after Downing Street defended the decision in 2010 to destroy the landing cards that recorded the arrival of the immigrants.
The Windrush generation came to Britain from the Commonwealth after the Second World War and are named after the ship that brought one of the first large groups of West Indians to Britain.
Anyone who entered the UK before 1973 is legally entitled to live in the country.
But despite having been in the UK for most of their lives, many have begun to experience issues as a result of tightened immigration requirements.
It has seen some - who might never have felt the need to apply for a UK passport before - left without the documentation now required by officials.
As many as 50,000 are thought to be experiencing difficulties in finding work, getting NHS care, accessing benefits, or trying to secure housing.
There are even fears some may have been deported in error.
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Home Secretary Amber Rudd has said she did not have "any evidence" this had happened, but Cabinet Office minister David Lidington said on Tuesday that officials were trawling through files to establish whether there had been any wrongful deportations.
The Home Office has not provided details of the 49 new cases being investigated.
The PM has told Caribbean leaders she is "genuinely sorry" for the "anxiety caused" and said she wanted to dispel the notion that the Government wanted to clamp down on citizens from the region.
The decision to destroy the landing slips was taken for data protection reasons, according to the Home Office.
It said they "did not provide any reliable evidence relating to ongoing residence in the UK or their immigration status" and that it was "misleading and inaccurate to suggest that registration slips would therefore have a bearing on immigration cases".
The department stressed that officials consider alternative evidence, such as tax records, utility bills and tenancy agreements, as evidence of ongoing residency in the UK in these exceptional circumstances.
The PM's spokesman said the UK Border Agency had disposed of them in 2010, when Mrs May was in charge of the Home Office.
He said the slips provided details of an individual's date of entry, but not reliable evidence of immigration status.
He added: "It was done for, I think, reasons as well to protect personal information.
"The decision was taken to securely dispose of these documents, and that was the right one to take."
When asked if Mrs May had been aware of the disposal, he responded: "My belief, at this moment, is that it was an operational decision that was taken by the Border Agency."
Labour MP David Lammy has said "heads must roll" at the Home Office and shadow home secretary Diane Abbott labelled the revelation "truly shocking".
Ms Abbott said culpability for the "fiasco" rests with the Home Office.
She added: "The Home Secretary should immediately announce that she will accept the burden of proof in deportation cases like these lies with the Home Office, not with the potential deportee.
"And she should say what steps she will take to ensure that people who have a right to be here continue to enjoy free access to the NHS, and the freedom to change jobs, homes or bank accounts without further harassment under her Government's hostile environment policy."
:: The Home Office has set up a dedicated web page to help Commonwealth citizens confirm their status in the UK, which can be found here. Alternatively, call the Home Office helpline on 0300 123 2241.