Everyone is only going to be 'offered' the vaccine, not 'given it by the autumn.
So its reasonable to assume most of us will be waiting until what, this time next year perhaps. Which by then, questions will be raised presumably about the need for a booster shot for the vulnerable and elderly. So I can see a very long extension of restrictions, if only a parred down version.
I saw something briefly that work is being carried out in communities and sectors where there is a lot of suspicion of the vaccine (BBC R4?). This seems to be different from just the anti-vax narrative, and more about suspicion of institutions and government policy that have never served them well.
And no, you cannot demand that they get the jab or get the sack. That borders on eugenics and is absolutely not acceptable.