According to a recent Institute of Fiscal Studies (IFS) study, Indians make up one in 10 of all foreign-born doctors in the NHS and the British Association of Physicians of Indian Origin (BAPIO), which represents this group, is among the organisations campaigning against the "discriminatory" surcharge for some years now.
In a statement Boris Johnson's spokesperson said "The Prime Minister has asked the Home Office and the Department for Health and Social Care to remove NHS and care workers from the NHS surcharge as soon as possible".
"NHS and care workers from overseas who are granted visas are doing this already by the fantastic contribution which they make".
A spokesman for Downing Street said work by officials is now under way on how to implement the change and full details will be announced in the coming days.
The Prime Minister told Sir Keir: "I do accept and understand the difficulties faced by our wonderful NHS staff and, like him, I've been a personal beneficiary of carers who have come from overseas and, frankly, saved my life".More news: Calls for Dominic Cummings to resign after reports he broke lockdown rules
The current fee is £400 per year per person and is set to rise to £624 in October.
"Now we need the Tory government to scrap the NHS surcharge altogether, build a fairer immigration system, and show a meaningful commitment to NHS and care workers - including paying them all at least the Real Living Wage".
Labour, the Scottish National Party and the Royal College of Nursing have expressed the view that health workers should be exempt from the "unfair" charge.
Senior Tories demanded change, with former party chairman Lord Patten calling it "appalling" and "monstrous".
"So with great respect to the point (Sir Keir) makes, I do think that is the right way forward".More news: Premier League confident about June restart
Mr Johnson had said yesterday during PMQs that he understood the opposition to charging foreign NHS workers but said the United Kingdom must "face the realities" of the funding that the fee provides the health service.
William Wragg, the Conservative MP who chairs the Commons public administration and constitutional affairs committee was one of the first Conservatives to support the lifting of the surcharge for health workers.
"This is a victory for common decency and the right thing to do. We can not clap our carers one day and then charge them to use our NHS the next".
Unison general secretary Dave Prentis said: "This is long overdue".
Care workers, cleaners and porters had originally been left out of the scheme, which only applied to certain occupations including nurses, biochemists and radiographers.More news: Further drop in number of Coronavirus deaths in NI care homes