@0c1a9324 In England it seems to be being handled by your GP practice - I had my flu shot booked and got a text a couple of weeks ago saying that I would be offered a covid booster at the same time, but my MiL, who is with a different practice in the same village, hasn't. 

 @d6ed95e6 NHS Scotland has a centralized national booking system and GPs can't schedule vaccinations. (On the other hand they don't appear to have a mechanism for checking your eligibility claim against your medical records ...)