Nokes encouraged those affected to make contact with the Home Office and said the government is determined to help people build up a picture of their life in the United Kingdom even if they might lack the required documents.
Prime Minister Theresa May on Monday reversed an earlier decision and agreed to meet Caribbean Commonwealth leaders while they're in London for a summit this week.
"I do not want of any of the Commonwealth citizens who are here legally to be impacted in the way they have and, frankly, some of the way they have been treated has been wrong, has been appalling, and I am sorry", Rudd told parliament.
But Mr Lammy, who has led the cross-party charge to highlight the issue, hit out at the Home Office's response, branding it a "day of national shame" and accusing the Government's immigration policy of taking a hard-right turn.
"It is inhumane and cruel for so many of that Windrush generation to have suffered so long in this condition and for the Secretary of State only to have made a statement today on this issue".
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"People should not be concerned about this - they have the right to stay and we should be reassuring them of that".
'Can she tell the house how many have been detained as prisoners in their own country, can she tell the hse how many have been denied health under the NHS, how many denied pensions, how many have lost their jobs. And that is why I have acted. "That is why I am so committed to ensuring that there is no cost involved".
People born in Jamaica and other Caribbean countries are thought to be more affected than those from other Commonwealth nations, as they were more likely to arrive on their parent's passports without their own ID documents.
Immigration minister Caroline Nokes appeared to suggest that some individuals may already have been deported in error. The exact number of people without official documents is unknown.
The immigrants are named after the Empire Windrush, one of the first ships to bring Caribbean migrants to Britain in 1948, when Commonwealth citizens were invited to fill labour shortages and help rebuild the economy after World War Two.
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Most recently, she was admitted to Houston Methodist Hospital on Good Friday suffering from shortness of breath. She has also been undergoing a long-term treatment for Grave's disease, a life-threatening thyroid condition.
The British government has promised to act to reverse "terrible mistakes" made over the treatment of immigrants from the so-called "Windrush" generation, after revelations that people who came to the United Kingdom decades ago are being told to leave the country.
May's six-year tenure at the interior ministry was marked by a determination to reduce immigration numbers, something she has continued to emphasise as premier and in Brexit negotiations.
"We are not aware of any specific cases of a person being removed from the United Kingdom in these circumstances and we have absolutely no intention of asking anyone to leave who has the right to remain here".
The Home Office is also due to announce changes to the policy aimed at finding the "correct solution" for those facing action because they lack paperwork. "We will review any cases that are brought to our attention".
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