I don't know who the Nuffield Trust are, or how valid their research, but they seem to disagree with the concept that immigrants are what's causing the UK's NHS to have budget shortfalls. The much bigger issues seem to be an aging population, more expensive treatments and rising wages in the medical sector. It would seem reasonable that unless the immigrants are retirees they are probably paying enough taxes into the system to cover the costs of the services they are receiving from the system.
https://www.channel4.com/news/factch...ion-nhs-crisis