Having read all these I feel very humbly grateful for what our HC provides. (Re my emergency example, I didn't know what it was, or that is was life-threatening, until GP arrived!)
Many years ago DD2, aged about 5 months, had a funny reaction to her 2nd DPT, one of our GPs arrived in the middle of the night and stayed to observe her until she stabilised. We have also had a query appendicitis and again a GP came during the evening, poked, observed and waited and eventually said take her to A & E (they admitted her but it came to nothing.)
There is a pharmacy at our HC (3 practices I think) who will happily provide repeat prescriptions from a phone call (2-3 days usually.) They also dispense prescriptions for those who live outside town.
If you ring first thing and think your need is urgent then you will see a GP, often your own, the same day.
The HC has a treatment room which will deal with everything except probable fractures (no X-ray facility) during surgery hours.
The practice covers an extremely large rural area, and those living way out won't experience quite what we do, but I have to say I am very satisfied with the service provided to us. (Agree with bundle re Do Not Attends - what is the matter with these people???)
Not sure how this compares with yours, Susan?