Some are missing the point I think; this isn't a request to see a doctor privately, it is a request to use a piece of equipment. Paying the £1800 to lay on the machine is one thing; someone still has to read and interpret the results and that means the people with the machine :-/
Chris, if you were mine you would be down at the hospital having a choline PET as we speak. In your head the PSMA is best and will solve your problem but apparently your medics and CCG don't agree otherwise it would have been sorted. I agree with your onco that it is the GP's responsibility to refer you if a private session on the scanner is truly available but is it really? What I mean is, have you spoken to whoever has the PSMA tracer and they said "yes we offer private consultations for £1800" or did the CCG refuse you because it would cost them £1800 and you said "I will pay that"?
If the former, I agree with the onco ...GP should refer. But if the latter, it may be that there simply is not a system for the onco or CCG to pick up the bill and then transfer the cost to you somehow. Furthermore, because John was self-funding I used to get an itemised bill for everything he had. The PSA test cost £75 but then we also had to pay for all the extras (I can't remember exactly what they were but probably the syringe, the phlebotomist, for the the result to be uploaded onto the system, stuff like that)