I agree. Go in expecting support, rather than trouble. Most GPs these days are supportive, if not necessarily informed. When I told my new GP last year, I just said "Hello, I've just moved here, and I'm here to see you because I want to begin a gender transition." She replied, smiling, "Oh - it's been a while since I've dealt with one of those, but we can learn together!"
If you get a GP who does turn out to be a git, then just go and see a different one. All they need to do is to refer you to the district psychiatrist for assessment (this is just to ensure you don't have any mental health issues - or that if you do, they're going to be responded to alongside of your gender dysphoria, it's for your support). They in their turn will then refer you on to your nearest gender clinic for further assessment. It's not down the GP to have any opinions about what you're experiencing.
Which part of the country are you in?
(Incidentally, once the gender clinic takes you on as a client (which could take a few months after initially seeing them), you can generally get NHS funding for some laser sessions (I noticed you writing about hair removal elsewhere, you're a good candidate for laser with your hair colouring).
