I lived in the UK for 10 years and am from New Zealand, where we pay for our doctor's visits. It's $35 (about £17.50) for adults and recently free for children. Low income or high users pay a nominal sum.
I much prefer the system here, nearly all the doctors are great at my practice, you can always get an appointment on the same day or urgent appointments at weekends or evenings. The doctors always listen, examine and will prescribe where necessary. I've never felt rushed or fobbed off. If you don't see your own doctor, they have a meeting at the end of the day where they talk about consults. All follow ups are by your own doctor.
E.g. With DS1 in London, went to the doctor for reflux. Four appointments later, finally see a paediatrician at 4 months old to be prescribed Losec. No follow up even though we tried and tried as his pain never went away completely.
With Ds3 in NZ, at six week check up - I think he has reflux. Here you go, have some Losec and come back for a checkup. If he doesn't improve we will refer to a paediatrician
You can get almost anything on prescription, including paracetamol or nurofen for children or adults, my GP prescribed vitamins for PMT.
I had to go private in London once - letter required for flying and had to be within 48 hours before flight. It was really really expensive. The NHS doctor was also charging but it took three days to write it. There must be some medium out there.