Dr Joe Aldred spoke after a new report by MPs and peers found immigration officials "unlawfully" locked up two people, even though they had the right to be in the UK.
The Churches Together in England's lead for Pentecostal and multicultural relations told Premier: "Whenever somebody is at home and they are wrongfully detained, that is always going to be a trauma...
"Therefore, it is right that the background is investigated, and we find out why and what needs to be done about it."
The Home Office was responsible for "shocking" treatment of individuals who were locked up unless they could satisfy officials of their entitlement to be in the country, the parliamentary inquiry concluded.
It said: "Such an approach is simply unlawful - it is for the Home Office to satisfy itself that it has a power to detain an individual - not for an individual to have to satisfy the Home Office that they should not be detained."
Dr Joe, who is part of the so-called Windrush Generation which arrived in the UK from Caribbean countries during the 1950s and 1960s, said it was important to remember only a tiny minority have encountered problems.
He added: "What we find - from my own experience of working in the community - is that the vast majority of the Windrush Generation have indeed sorted their status and have documentation to prove their citizenship."
The Joint Committee on Human Rights focused on the cases of 60-year-old Anthony Bryan and 62-year-old Paulette Wilson - who each came to the United Kingdom from Jamaica in the 1960s.
It concluded both were locked up twice, despite case files showing officials discounted "ample information and evidence" backing their claims. They have each since received an apology from the Home Office.
The committee chair Harriet Harman said: "What happened to these two people was a total violation of their human rights by the state's most powerful government department.
"It needs to face up to what happened before it can even begin to acknowledge the scale of the problem and stop it happening again."
A Home Office spokesman said: "Our priority is to ensure that those who have struggled to demonstrate their right to be here are supported to do so and we have issued more than 2,000 documents confirming people's settled status.
"But we know that it is equally important that we ensure that nothing like this can happen again. That is why we are carrying out historical reviews of detention and removals and have commissioned an independent lessons learned review."
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