The number of “potential” Windrush cases reported to the Home Office has passed the 5,000 mark.
They are among a total of 13,000 calls to a specialist unit set up within the department after the scandal erupted last month.
The Home Office also disclosed that more than 850 people now have documentation following an appointment with the dedicated team.
The latest figures were revealed as Home Secretary Sajid Javid announced that legislation has been introduced to bring into force a package of measures designed to help end the crisis.
Under the Government’s scheme, fees for citizenship applications will be waived for Commonwealth nationals who settled in the UK before 1973 and children of the Windrush generation who joined their parents before they turned 18.
I want to swiftly put right the wrongs that have been done to this generation and am committed to doing whatever it takes to make this happen.Sajid Javid
Applicants will need to meet the good character requirements in place for all citizenship applications – but they will not need to take a “knowledge of language and life in the UK” test or attend a citizenship ceremony.
Members of the Windrush group who have left the UK but are seeking to return will be able to apply for relevant documentation free of charge.
Mr Javid said: “I am clear that we need to make the process for people to confirm their right to be in the UK or put their British citizenship on a legal footing as easy as possible. That is why I have launched a dedicated scheme which brings together our rights, obligations and offers to these people into one place.
“I want to swiftly put right the wrongs that have been done to this generation and am committed to doing whatever it takes to make this happen.”
Ministers faced a furious backlash over the treatment of the Windrush generation – named after a ship that brought migrants to Britain from the Caribbean in 1948.
While many of those who arrived have taken British citizenship or have official documents confirming their status, others have struggled to produce paperwork demonstrating they are lawfully resident.
People who have been living legally in the UK for decades have lost their jobs, been denied access to NHS treatment, benefits and pensions, had their driving licences withdrawn and been warned they face deportation.
Last week it emerged that 63 cases are being investigated in detail as part of efforts to check whether anyone was wrongly removed or deported as a result of the failings.
Meanwhile, the Home Office announced a number of senior staffing changes on Thursday, including the departure from the department of director general of immigration enforcement Hugh Ind.
Mr Ind, who is moving to work at the Cabinet Office, was one of a number of officials questioned by the Home Affairs committee over Windrush and removal targets.