Same here, there's a vaccination center 10 miles from me, but, as the programme has progressed, it's specialised as a Senior Citizens and vulnerable centre, I have to go 25 miles to a local racecourse.
I believe there's some seriously intelligence led mathematical modelling going into the roll out, so we just need to be thankful dumb sheep and show up when and where indicated!
I booked mine via the online portal and it's amazing how it works, the dates and time slots change by the second, as people book and cancel, then rebook.
How it works without crashing is beyond my pay grade to understand ... Like I said, sheep mode, do as I'm told and be very grateful!