The Windrush scheme will be given baseline funding of £200m but will be uncapped, home secretary Sajid Javid announced on Wednesday.
The funds will be available to anyone in the UK since 1988 who was erroneously targeted by immigration officials, and claims will also be accepted from the families of victims who are not longer alive.
Javid told the Commons: “Nothing we say or do will ever wipe away the hurt, the trauma and the loss that should never have been suffered by the men and women of the Windrush generation, but together we can begin to right the wrongs of Windrush.”
“There is no cap on the scheme, so no one knows what the eventual cost will be. It will be based on people’s needs and the claims that are made by eligible people, but the baseline estimate from my department is that it will be approximately £200m,” he added.
Critics pointed to the fact that legal fee reimbursements will only be given “in certain circumstances” and will consist of a “fixed amount”.
Labour’s David Lammy said it was “deeply unfair that the legal fees of the victims will only be repaid up to a capped amount”.
Others called for the scheme to be simple and accessible.
Carole Williams, Hackney councillor and cabinet member for employment, skills and human resources, said: “It needs to be simple, straightforward, with no complex web of bureaucracy to act as a barrier for people to access the redress they are entitled to, and with support, including legal aid, for those who need it.”
When pressed in the Commons, Javid failed to say whether legal aid would be available for claimants who required it.
He said: “We are looking carefully into what kind of support is needed, because some cases will be less complex. We want to make sure that people have help, if they need it, to put their case together. We want to make sure that no one is denied justice and that people can make a proper claim.”
A Public Accounts Committee report in March found that the Home Office was “shirking” its responsibility to Windrush victims and shifting pressure to local authorities.
