There is more than one variable at work, besides vaccination. Obviously, Delta is a difference.
But significantly, this time last year was a lull between waves. Very different, if you compare it to November, when no one was vaccinated.
Beyond just raw total case numbers, there is a clear vaccine protective effect in UK cases, hospitalizations and deaths between the vaccinated and unvaccinated - as there is everywhere else. The higher case numbers now (as compared to a certain particularly unflattering select snapshot in time) are not because of vaccination.
IF the virus behavior and human social behaviors were constants, and IF we were soon comparing, say, November 2021 to November 2020 (your example for the UK), then maybe a valid comparison could be made.