For NHS gender services in England, the route is moving to GP referral only. Self-referral, which used to be available at several clinics, is being phased out. A useful referral letter from your GP usually includes a basic gender history, any relevant physical and mental health background, and a clear request for assessment at a Gender Identity Clinic.
If your GP is hesitant, "advice and guidance" routes, where the GP can ask a specialist a question before referring, are increasingly available. You can also ask politely about the practice's experience and, if needed, request to see a different GP at the same practice.
Once a referral is accepted, you join the waiting list. Where you are in the queue depends on when your referral was received and which clinic it went to. A single national waiting list is being introduced, which should make movement between clinics more transparent.