There's some interesting discussion about this on gov.uk.
Broadly speaking, it makes sense to work backwards from the statistics on likelihood of death/serious illness and vaccinate people accordingly. So care home residents and their carers first; then frontline NHS staff and the over-80s; then over-70s and so on. NHS workers aren't particularly at risk, but a) they look after their own and b) they get vaccinated against and tested for all sorts of infectious diseases as a matter of ethos - it's not a good look to infect your own patients. Bus drivers (who were disproportionately affected) don't get a mention, poor sods.
The original discussion also pointed out that people in 'BAME groups' are more likely to die or become seriously ill than whites, so maybe they should get priority. It didn't actually mention the fact that men seem to be worse affected than women, but the same principle applies. Neither of these factors made it through to the final priority list, which is a bit of a slap in the face.
They should have done a proper points system. So many points for every year of age and additional points for BAME people and men. So a black man ranks equally with a white man who is a couple of years older, who in turn ranks equally with a women who is a bit older than he is.
This would be the sensible thing to do, with the bonus fun factor that we'd see a bizarre coalition of racists and feminists whining and moaning! And probably the SJW finding some angle to moan (it's condescending to BAME groups; it suggests that they can't look after themselves properly?).
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