I don't know if this will matter as I'm in another country but I got a referral from a local GP to a local psychiatrist, who had dealt with gender issues and both of which I had never seen before.
Got assessed in 2/3 sessions (1 week, because I'm impatient) and she wrote a letter to my new GP, who works in sexual health, who prescribed T, after some bloods and general health session with a nurse. I have never seen a 'therapist' if that's different I don't know if you have different meaning etc. But the only person I talked with about my gender issues was the psychiatrist.
As said some people can get around it by signing a waiver saying they have demonstrated informed consent for the therapy they are wanting - but I would assume that GP is a very liberal practitioner and not pin my hopes on that. But stranger things have happened I guess...