My doctor is an NHS practitioner. If I have an "emergency" and need an appointment, I can get one that day. Otherwise normally it's a weeks notice give or take. I don't pay anything to the doctor, or to the practice, (other than my National Insurance contribution which is taken out ore tax).

I do have private health cover but it doesn't help much if I have a chest infection. If I need an MRI or to see a consultant, I can effectively skip the waiting lists and go to a private hospital, but if I have a heart attack or any immediate emergency, I'll be going to an NHS hospital regardless.