I don't know how it is in the UK (I expect similar), but here in Canada, there is essentially no difference between the public health care system and the private sector. Both follow the WPATH guidelines. The big difference here (and, I suspect, over there) is that the waiting lists are shorter for the private sector. I was able to get in in three weeks with a private therapist, where the public system would have made me wait three months. But the care I received was equally good.