GICs are specialists whose job it is to help you decide if/what surgeries etc you want, not GPs/ MH. The GP and/ or mental health can and should refer you directly to them.
I'm not NHS England, but I was referred to MH and had two unnecessary sessions with an untrained psych during which i mostly explained to her what being FTM meant and what medical options there were. It saved no time when I got to the GIC and achieved nothing.
the mental health person should be helping you with anxiety but not holding back your GIC appointments, especially if they're not trained in transgender care