The Shadow Attorney General Baroness Chakrabarti has urged the government take action after the "unacceptable" treatment of the "Windrush generation".
She said: "I share the honourable gentleman's admiration for the people who came here from the Caribbean and contributed so much to our society in many many different ways".
The article comes after the prime minister reportedly agreed to a request for talks with Caribbean officials over the issue at the Commonwealth summit - having first rejected it.
Dubbed the Windrush generation after the cruise ship that brought one of the first large groups of West Indians to Britain, anyone who entered the United Kingdom before 1973 is legally entitled to live in the country.
The issue of the children of Windrush generation migrants experiencing serious immigration issues in the United Kingdom, despite having lived here all their adult lives, will be discussed on the fringes of the Commonwealth heads of government meeting this week. But many arrived on their parents' documentation and never formally applied for British citizenship or a passport.
Their problems include difficulties when finding work, getting NHS care, accessing benefits, or trying to secure housing.
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".
"We want people to have confidence to come to the Home Office, we want to give them a message of reassurance, because we value these people".
Amber Rudd, the home secretary, will face MPs for Home Office questions at 2.30pm in the House of Commons and is expected to receive heavy criticism.
International Development Secretary Penny Mordaunt told BBC Radio 4's Today programme: 'People who are in that situation, there is absolutely no question of their right to remain, and their right to gain access to services such as healthcare.
Some members of the Windrush generation have been wrongly deported, Immigration minister Caroline Nokes has appeared to confirm to ITV News.
"Theresa May must apologise for this mess which has taken place as a direct outcome of the hostile environment she created".
The Home Secretary admitted she did not know how many had been deported.
Those born in the West Indies who settled in the United Kingdom throughout the 1960s are now generally referred to as the Windrush generation.
The Home Office's renewed guidance, published last week, offers no security or certainty.
The Government has been accused of being "cruel and inhumane" after many long-term immigrants who arrived from the Commonwealth as children have been told they are in Britain illegally.
Downing Street reversed a decision for Theresa May not to meet Caribbean leaders over the problems faced by the Windrush generation. The burden of proof must be changed and an apology must be made for the undue suffering caused by this heinous example of Home Office inhumanity.
The Prime Minister will now meet with the leaders on Tuesday.