Charing Cross Gender clinic is inundated with referals, as is common practice with NHS referals if you fail to turn up for an appointment or fail to request an alternative date, they will refer you back to your doctor. the pont being that if you cancell the appointment they will bring someone elses appointment forward.
Morally if one can afford to go private, it makes way for someone who cannot afford it. also it is more expediant, most people I have talked to had good experinces with Charing Cross, some of who'm went on to go private for their surgery,
electing for a procedure that they found was not available on the NHS.
I originally attended CX, was referred to the Gene clinic at Addendbrooks hospital, then went private from thereon to Wimbledon Parkside and eventually had surgery in Berne, Switzeland.