The cheapest way to run an organisation is efficiently. The second thing, in the case of public services, is that they should not be run for a profit. While many goods will be bought from the private sector, if any part of the NHS is outsourced it should be to an organisation not run for profit, like a charity, not to a commercial company run for profit.
Dinahmo Many, and it may soon be most, who opt for private care do not do have health insurance and pay for it out of savings. They pay for it because the NHS cannot, or will not provide proper care within a reasonable time, for life-containing or very painful conditions and for most these are minor conditions like cataracts, where treating older members of society is considered unnecessary because they do not work and contribute nothing to society to make it worth while.
Delays in such operations as cataracts or carpal tunnel syndrome can have serious repercussions in older people and trip them up into being housebound, lonely and lead to a serious decline in their overall health.