Yep, the consultant can do the op on private or NHS I believe (He does both I believe). Obviously private = faster & more expensive while NHS = longer waiting & free.
Not medical advice, but what I did was to find a really good physio/osteo (Always helps if they do a lot of local sports people in my eyes) and see what they say. They can then refer you for MRI, consultant or may even be able to fix you through physiotherapy. As I say, not medical advice but this is where I started after being messed about by the NHS and getting sick of waiting. Each appointment cost £45 and I think i've had 4 or 5 so far to get to this point of being referred to a consultant.
From googling (This isn't really any use, I have no idea what surgery i'd need) I saw a local private hospital offering spinal decompression for around £7k, so yeah, whatever you have will be thousands if not tens of thousands if going private.
Hope this helps!