Nearly 3,700 people have been issued with British citizenship under a Home Office scheme set up in response to the Windrush scandal.
From May last year, members of the Windrush generation, their UK-born children, and those who arrived in the country as minors have been able to apply for citizenship free of charge.
By the end of January, 3,674 people had been granted citizenship.
Ministers faced a backlash over the treatment of members of the Windrush generation, named after a ship that brought people to Britain from the Caribbean in 1948.
Commonwealth citizens who arrived before 1973 were automatically granted indefinite leave to remain but many were not issued with any documents confirming their status.
A public outcry erupted after it emerged that long-term UK residents were denied access to services, held in detention or removed despite living legally in the country for decades.
However, only two requests for urgent and exceptional support were approved as of the end of January.
Labour MP Yvette Cooper, chairwoman of the Commons Home Affairs Committee said it was "completely shocking" that only two people had been accepted for help under the urgent support arrangements.
"We know the endless difficulties and destitution that Windrush families have faced as a result of Home Office failures, and yet they are still not getting swift and comprehensive support from the Government," she said.
'Lengthy and detailed consideration'
Home Secretary Sajid Javid said the majority of requests have yet to be concluded.
He added: "The taskforce are working closely with individuals who have submitted requests in order to assess the current circumstances and gather the necessary evidence to support the urgency of their claim.
"I would like to emphasise that all these cases have had lengthy and detailed consideration.
"Any decision made in these cases has been checked and challenged extensively at operational level and been approved at senior official level."
The Home Office added that a vulnerable persons team within the Windrush taskforce has already provided support to over 600 people, including referrals to the Department for Work and Pensions for benefit claims and advice and support on housing.
Last year the Government apologised over 18 cases where people were considered most likely to have suffered "detriment" because their right to be in the UK was not recognised.
Ministers are also preparing to set up a compensation scheme for those affected by the failings.