I can only assume that in the OP's case, they have probably run out of vaccine and are now waiting for the autumn deliveries in time for flu season.
Because we have all but stopped counting in the UK, we've no idea just how prevalent it is now. I bought a box of LFTs the other day in Boots at the suggestion of a GP, but I'm not sure if you can record the result either.
However, the OP may find this useful:
https://www.nhs.uk/conditions/covid-19/covid-19-vaccination/getting-a-1st-and-2nd-dose-of-the-covid-19-vaccine/
And from that:
"After 30 June 2023, you can no longer book a COVID-19 vaccine online.
After this date, you will only be able to get a vaccination if you are at increased risk from COVID-19, and in most cases, you will have to wait until the autumn.
If you develop a new health condition or start treatment that severely weakens your immune system, you may be able to get vaccinated sooner if your clinician or GP surgery advises it."
In other words, we're treating it like influenza from now on (which isn't to say it's the same as influenza).