> In the UK, private insurance usually requires you to use the public health system as a first stage, and only fall back to the private one for things not cover

> In the UK, private insurance usually requires you to use the public health system as a first stage, and only fall back to the private one for things not covered by the NHS. I don't think it is for things "not covered by the NHS". It depends on your level of coverage but typically you would go to the NHS first and then invoke your private coverage when you have a diagnosis in order the eg skip the queue. When a relative had a heart attack, he was put on a waiting list for a heart bypass - 1 year. When he invoked insurance, he got seen within a month - by the same doctor and in the same facility as it would have been on NHS. In a lot of instances the private health care system is just paying the public one for advantageous access to services.