Until the last year or so Daventry GIC had much shorter waiting times and I have a friend who went there, but I think that by now they'll be as slow as anywhere else.
Talking to the doctor should not be difficult - but doctors are people too and have opinions and attitudes - some are a lot more helpful than others.
If the doctor has never dealt with a trans-person before then there are pdf's on the NHS website to give guidance.
I would advise you to keep it short and to the point. GP's have limited time per patient and they will ask if they need extra information.
You're Manchester area? The trans-support group here just disbanded and will only continue to meet in a very casual, loose form.
There is a large Gay Village in Manchester - do you go there?
If you want company of people similar to yourself then Napoleon's is the bar particularly frequented by trans-people of all types.
[edit]
Forget what I said about Daventry
https://www.reddit.com/r/transgenderUK/ ... ing_times/