Hi Saiya. ^^
I'm in the UK too (in Scotland, which has a different NHS system). It took around 10 weeks for me to get my psychiatric appointment at the local mental health department after GP referral, and a further 8 weeks to get the follow-up psychology appointment (although they messed that up -- it should've been sooner). A few days ago, I received my referral letter from the national GIC, and if I'd waited until now, I'd have a further 12-month wait before my appointment with them. Fortunately, I self-referred to them in June, so my appointment is backdated and I 'only' have about 7 months left to wait.
Even more fortunately, I have a GP who has been willing to provide me HRT as bridging therapy in the meantime, but not everyone is so lucky.

I won't even be able to get on the waiting lists for surgery until I'm at the GIC, but at least things are moving forward for me in the meantime. I'm paying for my own hair removal, since I would have to wait for the GIC otherwise -- and I think they only provide 8 sessions anyway.