I am in the same locality as Nigel and the situation is nothing short of shocking.
My 95 year old mother (limited mobility, lives alone) was in the first tranche of vaccines and expected to get her call for a jab in September.
When she heard nothing she has twice contacted her GP surgery who said 'await your call'.
When my wife got her call (with appointment associated, 35 years younger and in good health) in Weymouth this week I contacted Mother's GP and was again told my mother should wait.
I have spent four days trying online and calling 119 (literally hours on the phone and conformed 'no appointments available in Dorset' !) and finally at 11.30 last night I went got an appointment booked online in Bournemouth. That will be a 2.5hr round trip for me to collect my mother and take her there.
The local pharmacy Nigel refers to is clearly swamped and we have no walk in centres offered in Dorset.
The first round of vaccinations, arranged at pace and run by volunteers worked a dream, so more time appears only to have allowed bureaucracy and muddle to develop.
So much for Climate Emergency and saving fuel if we are all doing this LoL.