Absolutely not. I said the same about care home staff. If you want staff to be vaccinated and a safe health and social care system, you need to use carrots not sticks and making it mandatory to have a vaccination which is effectively in trial phase until 2023 is not the carrot.
And for everyone saying health staff who aren't vaccinated shouldn't work - are you happy for 10-20% longer waiting lists, even higher staff shortages, your elderly parents not get the carers they need because 20% of staff have been redeployed because they declined a covid vaccination?
We cannot magic up health care staff, it takes 3-4 years to train an RN or AHP, upwards of 10 years to train a Dr. We cannot afford to lose experienced professionals because they don't want a covid vaccination.
I am fully vaccinated, and have had several lengthy conversations as a manager with the couple of staff (out of 80or so) who I manage to try to convince them to rethink and have it (with no success). But I will stand behind any of them to be allowed to make a informed choice, whether I agree with their decision or not.