My doctors used to have 5 gps and I used to see my own, unless I was in a hurry and saw whoever was free.
Now they have another surgery and there are about 10 doctors on the list, plus others - maybe they do not update the list of non-partners, or they are locums or whatever - don't know.
Now I can book appointments online so can see who the doctors are but there is not an appointment for the next week and a half. There will probably be some appointments if I ring up, but that would have to be urgent. When I had to ring up for urgent appointments post surgery, I saw the duty doctor on the same day or got a phone call and was fitted in outside the appointment system. I have also rung up at 6pm and been seen at 6.30pm for a kidney stone (actually, husband did the ringing - I was out of it!) so emergency coverage is good.
If I want to see a particular doctor, they only seem to be there for a couple of days (or less) every other week, so I have to choose an appointment way before I know I am going to need it - usually about 3 weeks but it has been 4. I currently have two that I like and who seem to work the same way, so I try and see one of them.