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The home secretary said she would keep “all immigration measures under review” when she was pressed on the status of all overseas health workers.
Ministers may also consider offering all migrant health and care staff a one-year extension to their visa – something only offered to doctors and nurses so far.
Praising “NHS heroes” who were “working day and night to save lives”, Patel said at Friday’s Downing Street briefing she would reconsider policy on British citizenship.
“Our immigration system is incredibly complex and I think this crisis has demonstrated that, and shown the extent of that complexity too,” she said.
“You’ve mentioned citizenship and changes that we could bring in – that would need legislation going forward.
“But, as I’ve said, we keep everything under review.”
Any changes to how the UK grants British citizenship would require legislation, she said, before again stressing everything was “under review”.
Patel has been under pressure to extend more immigration rights to health and care workers, such as porters, cleaners and those working in care homes.
Pressed on why only doctors and nurses had been granted visa extensions, Patel added: “The work we are seeing across the NHS is just absolutely incredible and I have also just made the point as well that this is difficult.”
Adding there were “complexities around immigration”, she said she was “looking at various scheme” and would keep “everything under review”.
“I’m working across government with my colleagues in the Department of Health [and Social Care] to look at what we can do in this particular space,” she said.
It comes after the government was forced into two U-turns this week on immigration policy for health workers.
On Wednesday, Patel extended the NHS bereavement scheme and offered all overseas health and social care staff indefinite leave to remain should they be killed by the virus. Had she not, families who lost a loved one to the disease may have faced deportation.
Ministers also waived the health immigration surcharge for overseas health workers, which would have seen them pay £628 to use the NHS.
The press conference took place after it was revealed there was no change to the UK’s R number – which represents the reproduction rate of the virus – as the UK heads into the bank holiday weekend.
The national R stands between 0.7 and 1.0, with science and health experts warning that any value above 1 could spark a second spike.
Health chiefs also confirmed on Friday that the number of people who have died in the UK after testing positive for coronavirus had risen to 36,393 – an increase of 351 over 24 hours.