I signed up for private health insurance when I had to take my wife to hospital in Croydon, Mayday, in 1989. That single day event was sufficient to be scared stiff if we ever had to go there "for real". The treatment of my father in law in East Surrey was appalling as well with the eternal waits for information from the cancer specialists, the delays in getting results and generally being kept in the dark and waiting for everything.
The fact that you can see a specialist next week, and not in 6 months, is very important to me. Also that you will get medication that is not available on the NHS as it is too expensive. I specifically selected a policy that has unlimited cancer care and access to everything that is available for as long as needed - not just a year that some cheaper insurance policies have.
For a small operation for my wife in Gatwick Park it was so much less of a scary place that to me it is worth it if you can afford it.
Not stating that the NHS is a bad place to be - just that you have to fit in their timescales and overcrowding which is not good.