You'll find an interesting review of public private provision by Martin Chalkley in this brief. It says:
Viewed through the lens of economics, concern over ownership arises from the impossibility of complete contracts between purchasers of health care and providers of health care. Were complete contracts feasible they would render the question of ownership redundant. But contracts will always be incomplete: it is not possible to specify in advance all of the relevant circumstances around the care of every patient who is to be served, so as to ensure that they receive appropriate quality of care at a cost that reflects complete efficiency and does not leave the provider either with unsustainable losses or supernormal profits.
But the existence of the collective purchaser(s) for health care means that purchasers have power that individual consumers in other sectors do not have. NHS purchasing arrangements have the potential to ensure that private ownership does not lead either to a ‘race to the bottom’ – sacrificing quality in order to cut costs – or to supernormal profits being earned – which would siphon off NHS funds that could otherwise be used to deliver more health care.And the final statement:
We conclude overall that when considering the ownership of health care providers in a publicly funded health care system, statements such as “public good, private bad”, or the other way about, are misplaced. All health care providers require regulation. All health care providers require carefully thought out contractual arrangements that recognise the incentives and constraints they operate with – and these do differ between ownership types. The collective nature of health care purchasing provides the means for achieving this.That's it. A clear message for any open-mind politician.