Victims of the Windrush scandal have been offered £12m in compensation so far, says the home secretary.
Priti Patel said £4.1m of payments had been made to 338 people affected by what she called an "appalling scandal".
But she told a committee of MPs that her department still had "a great deal of work to do" in "building bridges" with the community.
Labour said over 1,500 people were still waiting for their claims to be paid, which was "disgraceful".
Shadow home secretary Nick Thomas-Symonds said the government's handling of the compensation scheme was "heaping insult on top of injustice".
The Windrush generation are people who arrived in the UK between 1948 and 1971 from the Caribbean.
They were granted indefinite leave to remain in 1971, but thousands were children who had travelled on their parents' passports - so could not prove they had the right to live in the country.
Many were caught up in the Home Office's "hostile environment" immigration policies introduced in 2012, with threats of deportation.
And come 2018, it was revealed many had lost homes and jobs, as well as being denied access to healthcare and benefits.
A compensation scheme was set up for the victims in 2019, but for some it was too late. BBC's Westminster Hour found at least nine people had died while awaiting payments.
In December, Ms Patel announced the minimum payment awarded to victims would rise from £250 to £10,000, and the maximum from £10,000 to £100,000.
She also said the figure would be higher still in "exceptional" circumstances, with money coming through quicker than before.
The latest figures from the Home Office said £12m had been offered overall since the scheme started in April 2019, with £4.1m paid out.
But the department also said the pace of the scheme had quickened, with more than £1.25m paid out in January 2021 alone, and £8m offered to victims in just seven weeks.
Ms Patel said: "The changes we have made are making real difference to people and I am committed to ensuring more people continue to get the payments they deserve more quickly."
But pushed by Labour's Diane Abbott at the Home Affairs Select Committee about the number of people still waiting to be paid or not coming forward for the scheme, she said her department still had "great deal of work to do".
The home secretary added: "Engagement and outreach events are one thing, but also it is still building bridges within the community.
"We should always reflect upon the fact and look at the history of Windrush, not just at the Home Office but across successive governments that did nothing about this.
"Therefore it is going to take time.. to build bridges, raise awareness, give people trust and confidence about the scheme and the ability to claim from the scheme."
'Failure and incompetence'
But her counterpart on the Labour frontbench, Mr Thomas-Symonds said the Windrush Compensation Scheme "isn't worthy of the name".
He added: "For just £4m to have been paid out to 338 people, leaving over 1,500 people's claims waiting, is disgraceful and shows how terribly this has been handled.
"The home secretary promised to take charge of this issue - this is yet another example of failure and incompetence."