Each NHS member of staff can make their own mind up. I don't think there should be a covid vaccine mandate. They could have introduced a vaccine mandate as soon as the COVID vaccine became available, but they are now. I don't know why they didn't do so in 2020 or 2021. It's a puzzle.
If they do enforce the mandate they will be in a position to sack them so you've not got long wait for your wish to come true.