The last three times I have tried to make a GP appointment I have been offered 3:00, 3:10 or 3:20. Primary schools here finish at 3:15. I am always asked by the receptionist if I can get someone else to collect my children, which I have previously done - but it seems unreasonable to ask. I got around it once by phoning up much later (11:30am) and got offered a 4pm. Leaving it till late morning on the off chance is a risk, as I have been told before that all appointments have gone.
It seems they won't prebook, or fill cetain slots until other times for appointments have gone. You have to phone from 8:30 to get a look in on decent times - and as a mum I leave for school with two little ones at 8:30 to get them there in time for 8:50! It seems a bit unfair.