@samuri – you can pay privately for surgery but the same WPATH Standards of Care must be met before the surgery can take place. So, that means demonstrating to two different gender specialists, consistently for at least one year, that you understand the one-way nature of surgery* and desire the end result.
Once you have the two signatures, you can either join the long queue on the NHS and wait another year or two or pay around £13000. There are only two surgeons in uk so you get either one privately or not.
* or, as one of the specialist psychs likes to say, “it’s easier to make a hole than a pole…”
Rachel