Free visa extensions should be given to all foreign NHS and social care workers, a group of MPs has said.
It is "unfair" that some of the lowest paid workers face charges of thousands of pounds to stay in the country, ministers have been told.
The Home Office has given a one-year free visa extension for some staff in the NHS and care sectors.
The government said it was "incredibly grateful" to health and care staff working on the frontline against Covid.
But the cross-party Commons Home Affairs Committee said all staff in the sector should be covered in the scheme.
The Home Office's visa extension list was initially limited to NHS doctors, nurses and paramedics, but in April it was extended to include more NHS staff, such as radiographers and social workers, plus some social care staff.
But the list does not include jobs such as porters and cleaners.
For those eligible, the extension covers visas which expire between 31 March and 1 October 2020. The scheme has been extended to about 3,000 key frontline health workers, the government said.
But the committee said that excluding care workers and lower-paid NHS staff from the extension scheme "fails to recognise the scale of their contribution to the UK fight against Covid-19".
"Many of the excluded NHS employees - who include hospital porters, cleaners and administrative staff - are providing essential services to the NHS and its patients at this most trying time," the committee said.
"They are also more likely to be in lower-paid job roles, meaning that the necessity of paying visa renewal fees is a much greater financial burden."
Labour MP, Yvette Cooper, who chairs the committee, said the NHS and social care sector have relied on help during the coronavirus crisis from foreign workers.
"Excluding the care workers who hold dying residents' hands, the cleaners who scrub the door handles and floors of the Covid wards, or the porters who take patients to intensive care is just wrong," Ms Cooper said.
She said that she will table an amendment with cross-party backing to the government's Immigration Bill.
Last month, the government scrapped the immigration health surcharge for all NHS staff and care workers.
The Home Office has also extended its bereavement scheme so families of overseas NHS support staff and care workers who have died with coronavirus can stay in the UK permanently.
In its report, the committee urged the government to make it easier for overseas health and care workers to settle in the UK.
"We believe that people who have given so much, and in many cases risked their own health, for the nations and people of the UK should be assisted to become permanent members of the society to which they have dedicated themselves," the report stated.
A government spokesperson said: "We are incredibly grateful for all the hard work that health and care workers continue to do in the fight against coronavirus.
"Right across the immigration system we are supporting NHS and other eligible health and care workers."