Well your GP is correct, under NICE guidelines they simply cannot prescribe more than 240mg per day of DHC. A private doc may be able to give you a better script (as in stronger opiates) if you don't tell them you are an addict (private docs usually don't ask to see NHS records), but again this is very expensive and likely unaffordable.
It used to be you could just order a private script of DHC off one of those online pharmacies without your GP knowing anything but new regulations killed that loophole off.
It sounds like you're in a tough situation as your tolerance has increased to the actual therapeutic effects of your medication and your history of addiction means you're lucky to even be getting DHC really.
I can understand the temptation to try and get bupe in that case. It does manage pain very well for some people although not others.
But consider the long-term... eventually you will get a tolerance to that too, especially if you try to chase a high as well as analgesia. And in the end you end up stuck with a far worse habit as bupe is way worse to come off than DHC.
Maybe someone can kick in with personal experience here, does bupe cause less tolerance because it's a partial agonist? I'm pretty sure tolerance would eventually become an issue even if more slowly, no?
This is the nature of opiates, you chase and chase something that just keeps running away from you.
Wrt pain management have you tried using cannabis alongside your DHC? I have back pain that's on and off myself and honestly although I like the high from DHC (until tolerance hits) I am happy with the pain relief from weed which is effective and non-addictive. I asked my GP to taper me off my DHC script which I was originally planning to get upped to morphine because I figure this is a better long-term solution.
I know it's not a magic medicine that works for everyone but it does help a lot of people with chronic pain so it's worth trying with an open mind.