I have MS and have found the NHS fantastic. They've authorized all my drugs and I haven't had a fraction of the trouble I had with my insurers in the US. I've also gone private--for shoulder surgery. What I have heard is that for serious conditions--cancer, MS, diabetes--you want to be seen by a NHS specialist, preferably at a major NHS center. They simply have more experience.
The other thing to bear in mind is that private insurance will generally not pay for chronic conditions. So, once you are diagnosed, you need to go to the NHS.
Also, if you don't like your specialist, hospital or GP, you can change. If you have any problems, contact PALS at your hospital or your PCT.