I think my doctors surgery have a good system. If you're booking a non urgent appointment you're just booked in, no questions asked. If you say it's urgent then they'll take details, if the patient gives them, and the doctor will phone you back in the afternoon. Then it's down to the doctor to decide how urgent it is.
The surgery is also open until 6.30 three days a week and 8 o/c two days and until midday on Saturdays. That's loads of extra appointments compared to my old surgery.