Ok well first thing you should be prepared for, the NHS is hell on wheels and is certainly not a transexuals best friend.

That being said the staff who work for them, doctors, psychs etc.. are generally pretty supportive once you actually get an appointment unless you come across an ignorant gp or one uneducated on the issue of transexualism.
I went to see my doctor for the first time last year and it took 7 months between that first visit and my first appointment with the GIC.
I would consider going private if you want fast results because trust me expect a wait with the NHS although you will get there eventually.
As for what to say to your doctor, I would just be as honest as you can and explain how you feel and what your end goal is, how you would like them to help you etc..most of the good ones will take that as a cue to organise a referral for a psychiatrist for you who you will need to see a couple of times at least before you will get a referral to your nearest GIC.
Sometimes I do wonder if the bloody NHS isn't trying force some of us to take alternative measures like going private etc...