Friday marks seven decades since the generation began with around 500 Caribbeans disembarking the Empire Windrush ship in Tilbury Docks in 1948, two weeks before the health service was formed.
Theresa May, who was heavily criticised in the recent Windrush scandal, is among those to have thanked the generation for helping rebuild post-war Britain.
Four generations of Dr Ngozi Edi-Osagie's family have worked in the same NHS trust in Manchester, starting with her grandmother, Ruby Inniss, who worked as a hospital cook from the late 1950s after arriving from the Caribbean island of St Vincent.
Dr Edi-Osagie, a paediatric consultant, said her mother was a nurse and her daughter, 22-year-old Indidi, plans to work in the same trust which she has already volunteered for after graduating from medical school.
She said the Windrush generation's contribution has been "amazing", adding: "It propped up the NHS. I think people forget they contributed in lots of different ways it wasn't just medical and nursing, there were cleaners there were cooks, porters, they did loads of jobs."
She argued that a cap on doctors coming into the UK has been "detrimental" to the NHS and, while more homegrown doctors need to be trained, that it must be lifted.
The Government has since relaxed a cap imposed by Mrs May when she was home secretary, meaning the NHS can recruit thousands more medical staff from abroad.
The NHS celebrated its black and minority ethnic staff at a Windrush awards ceremony last week, during which a recorded speech from Mrs May was played.
She said: "Without you, the health service would simply not be the success that it is."
But palliative care nurse Simone Williams-Anglin, whose grandparents came from Jamaica during the Windrush, said Mrs May's words rang hollow because she created the "hostile environment" to immigrants blamed for the recent scandal.
"She was the one who made the mess before she was Prime Minister," said Ms Williams-Anglin, a mother-of-two from London.
"And now she's Prime Minister she's apologising for her own incompetence."
David Lammy, a Labour MP who has been a vocal critic of the scandal, has been among those praising the link between the NHS and British-Caribbean, saying his aunts were among those from the Caribbean to work as nurses.
"Some patients at first didn't want the black nurses to treat them, but they won them over with their huge dedication and I have no doubt that the NHS would not be what it is today without the contribution of that fantastic generation of hardworking Caribbean nurses," he said.
Additional reporting by PA.