Bridge St went to doing this a while ago. While it winds up my diary-driven organisational side not to be able to book something routine well in advance, in practice ringing up in the morning does usually get me an appointment at a time I can cope with.

There are some exceptions: the phlobotomy nurse has specific days and for some reason IUS fittings are routinely only done on one afternoon a week (perhaps because you need both doctor and nurse for that).

There's probably an NHS target for reducing missed appointments driving all this.

ISTR the excuse I heard was that all the students kept not showing up for their appointments, and they were less likely to forget within a day...