Labour MP David Lammy had co-ordinated a letter to the PM condemning the "grotesque, immoral and inhumane" situation.
The Home Office has announced it is setting up a dedicated contact point for people with questions about their immigration status amid increasing concern over the treatment of some immigrants who have been unable to prove their status.
Answering questions in the House of Commons later, Home Secretary Amber Rudd vowed to "find out if there are any such people who have been removed". He said: "This is a national disgrace".
Labour MP David Lammy was granted an urgent question today to ask the Home Secretary Amber Rudd how numerous Windrush generation have been deported, detained and denied NHS care.
"Can she explain how many have been deported?"
She told Channel 4 News: "Potentially they have been and I'm very conscious that it's very much in error, and that's an error that I want to put right".More news: Shire sells cancer drugs to Servier for $2.4B as Takeda circles
The Home Secretary said: "I wouldn't want anyone who has made their life in the United Kingdom to feel unwelcome or be in any doubt of their right to remain here".
She was told the Government's immigration policies had led to a "day of national shame". How many have denied pensions?
This gross injustice is not an accident or a one-off - it is a stark reminder of what happens when a toxic and insidious anti-immigrant rhetoric permeates our politics and migrants are blamed for the faults of governments.
"Theresa May must apologise for this mess which has taken place as a direct outcome of the hostile environment she created".
The petition calls for an amnesty for Windrush immigrants who arrived as children, adding: 'The Government should also provide compensation for loss and hurt'.
Shadow home secretary Diane Abbott demanded an apology from Theresa May over the problems faced by Windrush generation residents.More news: Trump calls Comey 'Slippery' in Twitter attack, ahead of interview, book release
"The Government must immediately guarantee that anyone who comes forward to clarify their status should not face deportation or detention, because as things stand today there are thousands of people who are too anxious about their future to come forward".
"That admiration remains in place".
In an attack on her own civil servants, and perhaps the policies of Mrs May, Ms Rudd responded: "I am concerned that the Home Office has become too concerned with policy and strategy and sometimes lose sight of the individual". This is about individuals.
"This is about individuals and we have seen the individual stories and they have been, some of them, awful to hear".
Changes to the regulations introduced in 2012 aimed at stopping overstaying affected their legal status - meaning that despite living, working and paying tax in Britain for decades, they were now at risk.
The Windrush migrants were advised that they need to produce evidence including passports, to continue working or receiving treatment from the NHS.More news: Concluding ceremony of Commonwealth Games held at Gold Coast
Many British residents who came from the Caribbean with their parents as part of a post-war rebuilding effort have been threatened with deportation following a tightening of the immigration rules.