I'd say yes, I honestly believe the NHS is brilliant (in most cases) and pretty speedy too, but, the stress of waiting to be seen can be very high and if you can afford to "jump" the queue then I think you should do it. Having had both my "children" (27 & 32) operated on in the last 18 months for the same condition I have to say the treatment, one private, the other NHS, was pretty much identical, private was quicker (obviously) but the after care was in my opinion much better on the NHS. The stress of waiting for the scans and operation on the NHS was very wearing for my son (and for us), having said that everything they did was brilliant, but as it was at the National Neurological Hospital in central London (near to Gt Ormond St) it was what one would reasonably expect.
Just bear in mind to get that level of payment out of a private medical insurance probably means you'd have to ensure you were covered for a major, possibly London, teaching hospital, otherwise it would probably be at a local Bupa/Spire hospital where they may not be able to offer the same surgeon/post operative support team.
Private is very good but sometimes only a major London or similar sized/experienced teaching hospital can offer what is needed, I would imagine Adenbrooke's is right up there with the best, just make sure the private band you're in covers that hospital if that's the one you think you'd want to use. My insurance provider has "bands" of hospital based on premium paid.
As for appointment times, both the private and the NHS ones were more of a "guide" time than an accurate reflection of actual "seen" time, then again we werent going to walk out

We were given plenty of time to ask questions etc and never felt rushed with either, maybe that was why they both ran late? Small price to pay I think. (sorry that was a bit of post and a smal rant

)
Matt