Exactly as people above have said, go down that route. I have **** health, and spent a lot of time in hospitals, while living in loads of different places across the world, and the NHS has some of the best cancer treatment I've ever seen. I have private health plans personally, but I would still opt for NHS if I were diagnosed with cancer.
Talk to your GP. If you're still not satisfied, you can always opt towards the "other" medical incentive - money. Go private, and they'll find anything and everything if it means the rats might make a few extra bob!
A little £800 bill of some medical consults, tests and such likes, might save your life, because it goes down on your record, and the NHS is obliged to help you from that point on.