A doctors concern should be to do what he's told, which for the NHS and Government should be to prioritise saving the lives of many, rather than one.
Ok, forget the group if you want (but mathematically this does not stand up), what about the individual?
What about taking blood?
What about cutting someone's chest open?
What about breaking someone's ribs to carry out CPR?
What about amputation to save an infection?
What about turning off life support, so that organs can go to others?
All 100% necessary for the greater good, and all probably much larger risk than any vaccine would ever be. None of those cause a risk to others either, but not taking a vaccine does.
"first, do no harm" is a myth, it's like people swearing on the bible, in most circumstances, it's not worth the paper it's written on.
Extremely low risk of harm is worth it, if it prevents more harm to the individual and also prevents more harm to 4 others.
A doctor should agree with it, they would probably prefer it, to not have ICU overrun with covid I expect.