I'm in the same situation. My diabetes consultant said the highest recommended dose for the indication diabetes was 5mg/ml, and only obesity specialists were allowed to prescribe the higher doses for weight loss. He said it was very frustrating for him, because he had so many morbidly obese patients who would really benefit from being on the higher doses. When I said I was thinking about going privately so that I could get a higher dose he approved wholeheartedly.
Though the first pharmacy I contacted (ASDA) took my money, then turned me down the next day when their doctor looked over my application. The reason given for turning me down was that I had diabetes, which baffled me completely. The damned drug was developed for diabetics.
I've shopped around a bit since the prices went through the roof, and Medicine Marketplace did the exact same thing. Took my money, then their doctor turned me down because I have diabetes. I think some of them just want to cherry pick the very lowest risk cases, and turn down anyone with any other ailments.
I'm on 15mg currently, doing two injections, one 5mg courtesy of the NHS for diabetes, and 10mg from a private doctor/pharmacy. Once I've reached my goal of a healthy BMI and healthy waist/height ratio then I'll cut back gradually until I'm only taking the 5mg injection from the NHS.
Though I reckon once the really effective pill versions of GLP-1 medication become available they'll be so cheap that the NHS will be able to hand them out in the same way they do statins.