They offer it at my work, but I've no need for it... the NHS works just fine for me.
Until you need an urgent test so that you can start treatment, but have to wait weeks if you want the NHS to pay for it. Or the treatment you want/drug, is not financed by the NHS.
My parents paid for me whan I was a child, we paid for our children. There is no way we would let our chilldren wait, nor us wait. Now our children are adults, they have private health insurance too, one through work and the other because they are self employed (a must for those who are SE as they can lose their business and income why they wait for treatment). And no, the UK does not have a benefit system that will give you money while you wait for your operation and can then start work and earn money again, that seems to be another myth: you need insuance cover.
None of the 4 NHS cover everything. Even in countries why they pay higher taxes and pay a monthly fee (health insurance) to that government, and medicals have to be passed to get a visa, they still don't cover everything.