Then while I am on pension I am back on the public system, I am making no contribution but using it most.
That would basically be a system designed to bancrupt the public but lucrative for private insurers.
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.
To be clear though, I'm fine with this - the NHS is for everyone and it should be funded for everyone.
In fact it increases your tax costs, because private insurance provided by e.g. an employer is treated as a BIK.