CAMHS & your GP really let you down - if only they'd known to refer you to the Tavistock when you first enquired at 16, things might have been different. But yes, the waiting times for GICs in the UK are ludicrous, and the waiting times have gone up everywhere over the past few years as increased trans visibility means that loads more people have come forward to seek help. But there are things you can do.
There are actually 7 GICs in England, and London has one of the longest waiting lists as it's the most famous one. You can see any one of them if you live in England (sadly, not if you live in Wales - they can only refer to Charing Cross). The Laurels (Exeter) has a current waiting time of about 7 months, and Daventry (Northamptonshire) have just written to their patients this week to say that their waiting time for a first appointment is about 4 months, which makes it the shortest waiting list in the country.
Here's a list of all of the clinics, with their approximate waiting times based on figures published last September (so they've probably gone up since then): Charing Cross, London (13 months); The Laurels, Exeter (7 months); Leeds (15 months); Newcastle (no figures provided); Daventry (4 months); Nottingham (6 months); Sheffield (10 months).
You're entitled to visit any English GIC if you live in England, so if you do and you want to be seen more quickly, get your GP to re-refer you to either Daventry or The Laurels and cancel your referral to Charing Cross. Just take your Charing Cross acceptance letter to your GP and ask them to re-refer you elsewhere.
Another alternative (if you can afford it) is to go to one of the private GICs in London, and you can do that from anywhere in the UK. Gendercare and Transhealth are both reputable clinics and they publish their fees on their websites, but they're between £200-300 for a first appointment, and less for follow-ups. However, their waiting times are also longer than they used to be (because yes, everyone's getting desperate with the NHS waiting times) but you'd still be seen within about 4 months. And they tend to move quite swiftly on the hormone front.