The British NHS system is pretty good, you first sign up witha GP then you are if needed put in touch with a consultant. Usually this would be within a Hospital nearest to your address. If however you need an operation you can ask for a different hospital but i believe you cannot ask for a specific Doctor. You can only get to see a specialist privately if your NHS GP writes to that Doctor.
It's a simple system that works for 95% of people, however you can not be referred by yourself.
Hope this helps, it does mean less choice but hey we all get the same drugs and care and we don't have to go without just because we have no private insurance.