I can't say for sure, but it seems likely to me that you may need to be referred to these clinics now by your GP or maybe even a general psychiatrist. The reason being that there have been a number of high profile GMC investigations into these private clinics because patients who have attended them have later had regrets and have made complaints that the clinics did not follow proper protocol.
I know of Richard well, because he bought his current practice off my best friend in the world Russell Reid, when Russell retired to spend more time with his friends

. Unfortunately I am aware that Dr Curtis has had a recent investigation, and hence has had to be pretty careful to obey the rules, such as they are. So I think you may find that you'll need an "introduction". Gendercare is also partially run by someone I know well, as he is one of my lecturers and clinical supervisors. I don't know for sure, but knowing the people involved I would also be extremely surprised if they will take self-referrals. Unfortunately, as I think I observed in a previous thread, this process is not a speedy one, and in many cases you do have to observe due process, which in the UK usually means getting a referral from your primary care physician. If you do that I'm sure you will eventually get a reply, but it may take a few weeks.