@taxguru "The private firms have obviously decided that the investment produces a large enough payback. If a private firm can do it, why can't the NHS do it and make a profit to re-invest in other NHS services? It's just political dogma holding it back."
The private companies cherrypick the profitable services - they have no interest in anything or anyone who is not a source of profit.
Why can't the NHS charge and make a profit? - because that is not the purpose of a taxation-funded service that is supposed to provide a universal service to everyone regardless of their ability to pay. Despite what the Free Market Conservatives will have people believe, "profit" is not the only measure of success - and in many cases it is an entirely inappropriate measure.
Anyway, your proposal that people pay a little more for a better service is actually the point of the original question. The difference is that you seem to be willing to pay more, but only if it benefits you personally - you don't want to share the burden of increased investment in healthcare with everyone else by paying a bit more in tax (or into a ringfenced fund as is usual in Europe).
You might want to ponder that the direction that the UK is taking is away from universal healthcare to a two-tier system akin to the American system. This is no coincidence - American interests see the provision of private healthcare in the UK as a huge goldmine waiting to be exploited and have spent millions trying to influence politicians. A quarter of Americans owe over €10,000 in medical debt - this is after their insurance policies have paid for some of the treatments. 55% of Americans have medical debt - the average is well over €2,000. These are just the people who have actually decided to have treatment. There are millions who have decided not to be treated at all simply because they cannot afford the cost.
Think about this when Hunt tells you that he's "given" the average person £450 in NI reductions - the price of which is longer waiting lists, crumbling hospitals, outdated equipment, hundreds of thousands of unfilled vacancies in healthcare and social care etc. (But it was nice of him to reduce CGT on second homes, given that he owns so many that he forgot to declare them all).