If you're likely to be going to Charing Cross (CX) GIC, here's a rough timetable of what you can expect:
Firstly, your GP has to refer you to a local psych. Depending on what area you live in, this may be a gender specialist or may not be. Waiting times for that appointment will vary, but could be around the 6 month mark - I think that's roughly what mine was.
Then, the specialist has to refer you to CX. I think waiting times are currently about 6 months or so, but first you'll get a letter with a questionnaire to complete. Once you've sent that back, you should get a letter with an appointment date on.
A date for your second appointment at CX will be given to you after your first appointment (provided the computer systems at CX aren't down!) That's likely to be another 6 months or so later - and if all goes well, that's where you'll be given the go ahead to start T. CX will then send a letter detailing the dosage etc to your GP, along with a copy for you - when you receive this you can go to your GP and they should write you a prescription and sort out your first shot.
Alternatively, if you decide to go privately, you can make an appointment with Dr Richard Curtis at the Transhealth clinic in London. Last I heard, he charges £220 for the first hour. If he's satisfied that you've been living as male for long enough at that appointment you might get T straight away. Otherwise, he'll probably ask you to return in 3 months or so for a 30 minute appointment which will cost £110.
If you do decide to go privately for T but want to use the NHS for surgery, I'd recommend that you continue on the NHS route at the same time as starting T privately - don't lose your place in the system because if you do you'll have to start back at the beginning again.