There's the Choose & Book system of hospital appointments now, which tries to ensure that patients get a convenient appointment (to them), but I don't think it always works. Imagine if you, say, have an important commitment on a Tuesday morning, and your consultant only does clinics on a Tuesday morning .... Well, I know you can ditch your Tuesday commitment for once, but it's difficult for some people.
Anyway, patients do now get copies of letters that a hospital doctor sends to the GP, with all the details. I do agree it can be scary, with all those long words and medical terminology, but where I work, the patient gets a completely separate letter with all the scary bits taken out.