I think I'm very fortunate with my GP practice: never have difficulty getting through; can get a telephone appointment within a day (slightly longer if you want a specific GP); GP will arrange to see you quickly if required but often not necessary; can get a face-to-face appointment within a week if preferred (again, slightly longer if you want to see a specific GP).
Nurse or phlebotomy appointments are within a week - either at the practice or at a (local) hub.
"Our" GP is now senior partner. We've been seeing him for over 30 years - so we are now worrying about the fact that he'll be retiring soon (he must've been newly qualified when we registered with him). But at least the rest of the GPs in the practice will have been in part trained and/or recruited by him.
He started doing telephone appointments about 10 years ago so was ahead of the curve.
All my recent experiences of A&E recently (with ds' girlfriend) have been positive, as has dh's recent total hip replacement (12 weeks ago tomorrow).
This is central Glasgow, so at least I don't have the problems that rural patients face.