I'm a member of my local "Patient Voice" and this question has come up.
The Clinical Commissioning Groups have delegated the organisation of vaccinations to various groups of GPs. It seems to be a bit of a postcode lottery, but each GP group is responsible for trawling through their records to find the people who are eligible.
In most cases, people in care homes have been problematic, so over 80s have been called in. The groups have been issued with a certain number of doses, but if they don't have many over 80s on their lists, they've called in the next people in priority. Hence, some over 70s have been contacted.
Sometimes, they haven't been able to contact people and have had doses left over, which need to be used in a short time frame. That's why some people have reported that the fire service (or others) have been contacted.
I expect it depends on your local area (and/or country). Maybe look on the website or contact them if you're really concerned.