The advanced research centres are all NHS as far as I know. There are very few private hospitals indeed and none of them dealing with anything other than elective, mostly plastic, surgery. The NHS = 95%+ of health care and most private patients get a private room in an NHS hospital using NHS staff.

NHS pay you? for - what? No, never, never heard of such a thing, why? Really, I never heard of that at all! Why would they do that, I am confused!