First of all, there will be those who don't have any insurance.  Fecklessness, laziness, mad optimism, or plain old poverty could be reasons for this.  This gives us a base of people who don't have any healthcare (though I am going to assume some sort of A&E style healthcare will still be available).  It may be that there is also a 'provider of last resort' kind of thing going on, perhaps (again) mopping up the unclaimed vouchers, but I'll come back to that later.

After this first group, we have those who have paid for the bargain basement level of cover.  Again, this is likely to be dictated by salary, so we can probably assume this group will be located in geographic clusters.  At the moment, we have a system where the NHS tries to ensure that GP practices are spread around, so that there is a local surgery for most people.  Now, in the new system, GPs will have to compete with other GPs to either attract lots of clients, or to attract insurance companies to hire them on retainer.  Given that there are likely to be clusters of people paying the bare minimum, this means for a GP to be attracted to be in such an area he either has to have a hell of a lot of clients (as each one contributes a small amount) to forgo being in a more lucrative area, or, another possibility, be of inferior quality and thus forced to offer his services more cheaply.

Now, imagine one of a GP's patients is ill, and needs to be referred to hospital.  It may be that the insurance company (either the GP's or the patient's) requires treatment to be at a certain hospital, or even by a certain consultant.  In that case, the price for each procedure will likely have been decided already between the insurer and the provider.  Or it may be that the insurer only states the lowest cost provider should be used, which means a quick ring round to find out who that is at the moment.

Now hospitals in this system are likely to be placed somewhere with good transport links, just like branches of Ikea.  This enables them to cover a greater area, and so have a wider possible client base.  Thus a client may have to travel from quite some distance, and do so regularly if treated as an out-patient.  (Presumably this will be more common, as this translates to reduced costs for the insurer.)  The hospital, of course, will be seeking to charge the insurers as much as they can to maximise profit.  In an area served by only one hospital (as most places are in the current system and thus presumably would be at least in the early days of a new system) this translates to a level just below which it would be cheaper in a short enough timescale for an insurer to build a new hospital, fit it out, and recruit the staff.

Essentially, I do not see how healthcare can work as an efficient market which also leads to the best health outcomes.  The disconnect between the recipient of the services and the purchaser of the services is too great, and the frequency of a recipient accessing those services would )hopefully...) be low.  Thus, it is in a company's best interests to keep prices down even to the point it begins to effect the quality of service.  As long as the churn of customers this causes (either through direct experience or bad publicity) is not so great as to have a cost greater than paying for higher quality, it will happen.  Or, of course, you put in place regulation forcing higher quality, in which case the cost of premiums goes up, and more people drop out of the bottom of the system into the pool of uninsured.

A possible solution to this pool of uninsured, and a method of keeping quality higher, is to have a provider of last resort.  Assuming this is government owned, it would provide basic medical care, though presumably either not for all illness, or not all treatments, or at low quality (otherwise why would anyone pay for different cover?).  But how would this actually work?  I can see three possibilities.

Firstly, this rump NHS could continue to operate from current hospitals, while private insurers have their own hospitals.  Given that the number of people using the rNHS will be smaller than now, this will give the rNHS higher running costs per patient head than currently, leading to financial pressures - not conducive to forcing the quality of care up.

Secondly, the current hospitals could be sold off to private industry, and the rNHS becomes just another purchaser of services, like any other insurance company.  This would essentially make whoever ended up owning each hospital a monopoly supplier in their locality (given healthcare purchase is not particularly geographically flexible) and the associated regulatory burden to handle that situation.

Thirdly, the rNHS could maintain the hospitals as in 1, but additionally sell services to insurers.  Given the current spread of NHS hospitals, this would make the rNHS the monopoly supplier across the vast majority of the country, enabling them to dictate terms and prices.  However, the government could choose to keep prices at some internally defined level.

So, problems/queries.

1.  Who chooses GPs?  Insurers or patients?  If insurers, how do we ensure high quality, given they are not the recipient of the service?  If patients, how do insurers ensure there is pressure to keep prices down?  If patients choose and pay, how do we ensure it doesn't drive the sick poor away from seeking treatment?  Or do we keep GPs in the rNHS?

2.  How do we ensure a fairly even geographic spread of GPs, even in areas with few clients?  On the whole, I'd say having this is a good thing - reduced travel time for the sick, better placed to assist in public health matters (e.g. vaccinations, health advice [presumably provided under contract from the newly shrunken DoH], monitoring of communicable diseases, etc.), and so forth.

3.  How does the interface between GP, insurer and patient work when referring patients for further treatment?  If GP paid by insurer, there is pressure to keep costs down.  If paid by patient, pressure for medical quality irregardless of cost to insurer.  If paid by rNHS, is the GP ambivalent to cost to insurer?

4.  Who owns the hospitals?  If a private company, how do we deal with the local monopoly situation, the lack of competition?  Is a situation of a large number of local monopolies desirable?  If the rNHS own the hospitals, do we sell excess capacity to insurers?  If so, how much for?  If the rNHS isn't allowed to charge whatever it likes, either by diktat or regulation as a monopoly supplier, doesn't that remove price signaling?  Is a national monopoly of healthcare provision by the rNHS, paid for by private insurance premiums, intrinsically better than a national monopoly of healthcare provision by the NHS, paid for by National Insurance / taxes?  The problem here is that the barriers to entry into this market would be remarkably high.  The financial cost, and gamble, of building a new, competing, hospital would be immense.  Planning restrictions may make finding an appropriate site very difficult.  Regulatory concerns (I'm assuming there would be some) are another hurdle a new player would have to face.

5.  Assuming a provider of last resort status for a rump NHS, is it actually possible to allow a hospital, whoever it is owned by, to fail and close, without adequate alternative arrangements already in place?  If not, and given the high barriers to enter the market for a new hospital provider, how would 'creative destruction' enter the system?  If so, how do you guarantee service to uninsured?  Or do you not guarantee it?

6.  Would any mixture of the above options actually be more efficient than a central bureaucracy?  GPs will need to be regulated and paid, as now, though where the pay comes from may change.  Referring a patient to hospital will require the exchange of billing information.  Insurers will need a bureaucracy to deal with billing, with contracts, with sales, with marketing, with retention, with quality control.  Private hospitals will require the bureaucracy required to run themselves, as now, and will also need to be monitored and regulated, as now.  Ditto for rNHS hospitals.

But essentially, most of this argument is irrelevant.  Here's the shocker: I agree that free markets are an incredibly efficient method of allocating resources.  It works from crude oil to lard, from gold to manure, from Stilton to cheez-strings.  They lead to all of the good or service in question (assuming there is sufficient demand) being distributed, with the final determinant being what people are willing to pay.

And that is the rub.  Free markets don't find this level, this efficient distribution, through magic.  No capitalist fairy comes down and sprinkles efficiency dust over the system.  No, the hard work, the thinking and decision making, are all outsourced to each and every one of the participants in the market.  They make a decision on whether to buy or to sell, and many participants making those decisions over and over, a vast amount of human thought, leads, finally, to the level that just enables all those willing to pay the right amount to get what they want.

And so, if you want a healthcare system where the treatment you get is, ultimately, based on the amount you can pay, then yes, a free market is the most efficient way to achieve that.  Money, that handy little shared delusion we all have, is the tool you can use to share out this particular commodity.

But, and it's a big but, it is only one way of deciding how the commodity is delivered.  The NHS was built on the exact opposite principle, that money should not be how healthcare is divvied up, that rather a fairer system was preferred.  That it didn't matter whether you were a stockbroker or a bin-man, when you became ill it was in society's interest, in all of our interests, for you to be treated to the highest standard possible, to be treated equally, to be treated as a human being, not as a rational player in a free market.  That healthcare provision is special, because it deals with life and death.  That no-one should have to suffer illness or even death because they didn't earn enough.

And that isn't a rational judgement.  It doesn't stand or fall on financial benefits to the country or to tax-payers.  It is a moral judgement, and like most moral judgements you either agree, or you don't, and no amount of debate will change your mind.

Now, if you accept that proposition, as many do, you are left with the problem that the tool traditionally used to allocate resources is of no use to you, but you still have the problem of trying to allocate a resource along a different principle.  You need to simulate, in some way, the myriad decisions and thoughts made by perhaps millions of people in a free market, but while a free market can use money as a proxy for value, enabling the players to express how much they value a good, you are left with no proxy for fairness.  And so you have to build a bureaucracy, and provide central planning, to try and allocate healthcare in a fair way.  It won't be perfect, far from it.  It will be expensive.  And, of course, people will tell you it is inefficient (though I'm not convinced it is more inefficient than the possible alternative, as rambled about above).

But that is missing the point.  If society makes the decision they want to allocate this resource on the basis of need, and fairness, then you have to pay to create a system of allocating resources.  Yes, you want to make the delivery as efficient as possible, the interactions with the outside world of drug companies and so forth as efficient as possible, but the basic premise of the allocation system is intrinsically incompatible with free market analysis, because we have no way of converting the value of fairness to a society into cash terms.  Without that value in the equation, the allocation system is always going to look inefficient.  I know this.  I accept this.  Because I believe the cost to society for making health dependent on wealth is far greater than the cost for not doing so.  And I still believe this, even though I can't point to it on a financial balance sheet, because, ultimately, I believe a society is more than a group of individuals trying to make money off each other, and cost and value are measured by more than just pounds and pence.