Interestingly enough she went this morning, and got offered the 'flu jab too. I had a gander at the NHS app, and I see a note on mine that says "Patient specific direction to administer influenza vaccination" - so it looks like I'll be offered it too, which is good, as our local (Lloyds as was, but got sold to a local co Jardines) pharmacist doesn't have a timescale for 'flu vaccines yet. The pharmacy I'm going to (Lloyds as was, now Pyramid) didn't previously offer the Covid service.
Sometimes (mostly) the NHS works well despite the challenges.
ETA Despite it being near the end of the day my 4:20 appointment was about 4:28. Excellent.