In reply to WaterMonkey:
If she is registered with a GP, I'm sure she will get it.
I am 76 (77 this coming Saturday), as I understood it my local area was still concentrating on the over 80s, and I wasn't expecting to be called for another week or so. So I was pleasantly surprised when I got a text from my surgery last Tuesday inviting me to attend the local vaccine centre. I was offered 4 time slots, 1 for last Thursday and 3 for last Friday. I chose Thursday and duly attended getting my first dose of the Pfiser vaccine then.
It was all incredibly slick, well managed and straightforward.
There was a mix of age groups attending, so I don't think the centres are rigidly differentiating within the first 4 categories.
As I understand it some areas are getting well ahead of other areas, so many of the vaccine centres are now contacting everyone over 70, others are a few days behind.
Based on this I don't think your Mum needs to worry, particularly as she has already heard from her GP's surgery concerning shielding which indicates that she is on their radar.