There are only three options for surgery with the NHS. Oliver Fenton, Philip Thomas or Tina Rashid (under the guidance/supervision of Philip Thomas). You are given a choice of those three when you get to the referral stage, and it's up to you to do your research on them.
The NHS is still a bit stuck in the whole 'full time before hormones' thing, so it's often difficult to get them to budge from that. And they will generally time everything from the date at which you can prove you started RLE. For that reason I started my RLE way before I got my first appointment, and whilst I had to wait a year for that, I've moved through it all as quickly as is possible since. It's still taken a long time though. I'm at Leeds, btw. The people there are lovely and they will do their best to get people through as quickly as possible as long as they are convinced that it's right for the patient. I think they get a fair few people who go along having taken no steps forward themselves (eg coming out to family/friends/work, RLE, starting hair removal etc) and expect to be given hormones, and they are more cautious moving forwards with those people. I'm not saying it's right, that's a seperate debate, but it's the way they work. Your gp can prescribe bridging hormones but mine flat out refused; he said it basically wasn't an area he had any knowledge in and that he wasn't prepared to take on that liability, and instead he'd rather leave it to specialists. I tried a different gp at the same surgery and she said much the same. So it's pot luck really.
Good luck!