Depends on who you get referred to.
I take it you're trying to get in with Kneeshaw? He tends to insist on a referral from your GIC (not a GP), but you might be in luck if he's willing to accept written evidence that you've been diagnosed with GD; why not ring & ask his secretary? You'll also need to have been on T for at least 6 months.
Walls & Dabritz will accept a GP referral if you have an existing GIC diagnosis of GD.
If all of that is in order, then Mr Kneeshaw will see you within 18 weeks of receipt of your referral; Walls/Dabritz's waiting list is about 8 months from referral; Yelland's waiting list is now 9 months and rising.
In general, most of the male chest reconstruction surgeons won't accept GP referrals on the NHS; generally, they insist on the referral coming from a recognised GIC. Generally speaking, GPs can only refer you for breast reduction surgery which is not the same thing.
If Kneeshaw accepts your GP's referral, you'll need to phone his secretary as soon as you get the letter to organise your initial consultation.