I can only speak for Leeds but I know Nottingham works in a similar way.
First appointment is basically the initial 'getting to know you' with a care coordinator, who will do a risk assessment and ask about your history etc.
What happens next will depend on your situation. You may have a few more appointments with the same person or you might be put forward for a diagnosis with a psychiatrist/psychologist (I can never remember which sorry!). If you are diagnosed as transsexual then you are admitted into the care pathway and referred to the hormone clinic.
When I went for my first appointment, I had been full time for 8 months in all aspects of my life including work. I'd changed my name and had proof of all of this. I had no substance abuse problems or self harm issues or any other conditions that needed resolving. Therefore I was considered a 'straightforward' case and my second appointment was the diagnosis, and the third was with the hormone clinic and formulating a treatment plan with my care coordinator.
There are some people who don't get straight onto the care pathway, usually those who haven't made any kind of move towards living full time. Some people go to that first appointment as their birth gender and haven't come out to any friends or family; it's unlikely that person will be admitted straight away, and will instead have a series of meetings with the care coordinator. Once in the pathway if you are not full time then I doubt they will prescribe hormones. They are very cautious and prefer to be sure and safe; people complain about it but they see it as protecting both the patient and themselves. For me the GIC has been great, the people who usually get upset with them are those that aren't yet out or full time.
This is just my experience and understanding of it all, it does vary a bit from place to place.
