I am not sure how far you are into the process, but there is a wait between the 1st GP contact to the GIC taking you on as a patient - in my case it was 10 months. It has gone up since then considering how stretched NHS resources seem to be. However - this is the longest part of the wait, once the first appointment comes through and you get seen by a psychotherapist(s) things can speed up somewhat. It will still be some time before seeing the supervising doctor for the final decision on HRT, though (another 10 months in my case).
You should still be able to phone the GIC in question for some clarification or advice in the meantime, though. That's what they pay the person at the reception for. . .