The Windrush generation comprise people who came to Britain between 1948 and 1971 from the Caribbean, originally to help it rebuild after the war.
"It is a matter of denial of the dignity of citizenship, which really can not be restored", Jamaican Prime Minister Andrew Holness told the Good Morning Britain television show.
"It is only fair. Today it has 53", she said. "They find it hard to fill in all these forms to prove they can stay and they are being told they don't belong here anymore".
The four-page document, obtained exclusively by the Guardian, reveals Rudd promised the prime minister she would oversee the forced or voluntary departure of 10% more people than May managed when she was home secretary, partly by switching money for crime-fighting to her immigration enforcement programme.
She said: "These people are British, they are part of us, they helped to build Britain and we are all the stronger for their contributions".
Former NHS nurse Icilda Williams, who moved back to Jamaica in 1996 after 34 years in Bradford, said her annual visits to the United Kingdom to see her children had been halted since 2014 after she was denied a visa.
David Wood, the deputy chief executive of the UK Border Agency for almost five years until 2013, said the consequences for Windrush immigrants had not been foreseen.
Tighter border policies, which have left some migrants and their children struggling to prove their citizenship, are largely a legacy of May's time as Home Secretary - a role she held for six years before becoming prime minister in 2016.
That has become a problem since the introduction of Theresa May's "hostile environment" policy in 2012.
A former senior immigration official has said the impact of the Home Office's "hostile environment" strategy on the Windrush generation was awful but it was unlikely any individuals would have been deported.
At the time, most of these countries were still colonized by Britain, and so immigration status was not an issue.
"We have created a Britain where there is great suspicion of anyone who has a migrant background".
The Home Office said it would look into the cases of Ms Gocan and Mrs Williams as a matter of urgency.
The European Parliament's Brexit coordinator, Guy Verhofstadt, said full guarantees on EU citizens' rights were needed in the wake of the crisis.
Home secretary Amber Rudd.
As global alliances go, the Commonwealth is a loose network linking large economies like India, population 1.3 billion, with tiny pacific states like Nauru, population 13,000.
Earlier on Friday, Commonwealth leaders have declared Prince Charles to be the next head of the body after a personal plea from Queen Elizabeth.
Theresa May has said the decision was taken under Labour in 2009. May's government said it would lobby for Charles. "It removes any kind of incentive for it to survive on its own merits". "The Windrush scandal has taken the government utterly by surprise", Sophie Gaston, head of worldwide projects at the think tank Demos, told DW. And it may well be that the Windrush row will not affect such calculations in the end.
"The British government needs to deal with the situation expeditiously", said David Michael.
"But the truth is we don't know", he said.