Good news for me because 3 days after I got my invite to book my vaccination via the national site (which had no venues near me) I got today another text from my GP inviting me to book at the local vaccination centre which is 20 minutes walk from here. Yay!
I have my appointment for next Friday and then my 2nd is in July. Not sure which I'll get but probably the Oxford AstraZeneca. I have the following day off work in case I feel unwell afterwards.