The big issue with the privatisation of public services is that the profit gets transferred to the private sector but the risk doesn't. If your private provider goes under, the service still has to be delivered and the governmental body responsible for commissioning will have to pick up the tab for this. This happened with the waste and cleansing contract in Norwich. The provider went into receivership and the local authority had to hire in other contractors and vehicles to cover services they had already paid for. This is tricky enough when dealing with bins and street cleaning but try replacing a hospital at short or no notice
I don't think that analysis quite holds, as it's confusing different types of risk.
The risk that the private contractor faces is roughly the same risk that any entrepreneur faces: That their amazing idea will fail (their contract loses money) and they end up going bust and losing all the money (and time) they'd invested. And I'm guessing that's exactly what happened in Norwich: Company took a risk thinking they'd make a profit, and ended up making a loss. In one sense, when things work, the profit they make is the reward for taking that risk.
But of course when a company goes bust, the customers may also lose money and suddenly have to find someone else to take over their service. And that's the (entirely separate) risk you as the customer take when you contract out something. To some extent that risk is there anyway: Even if the Government or any public body does something in-house, it takes the risk that its financial calculations will go wrong, whatever it's doing will cost more than it expected, and it'll suddenly be faced with an unexpected bill to bail out the project. The only difference is, if you've contracted out, sorting out this situation becomes more complicated and expensive.
In terms of the pros/cons of privatising public services: What you're hoping for is that a private contractor will be able to innovate (or the threat of competition will spur them to innovate) in a way that saves you money compared to the Government just doing everything itself. There's also arguably a freedom issue: That if someone feels they have a great idea that will let them do something better than the public sector is currently doing it, then why not let them try? Contracting, to some extent, allows that. Set against that is all the additional bureaucracy associated with sorting out private contracts, possible issues of oversight of what your contractor is doing, and greater risks if things go wrong. With all those potential pros and cons, it's not immediately obvious whether privatisation is on balance good or bad for the NHS.
The trouble is, in politics today, the argument seems to be entirely ideological. The Conservatives assume, as an ideological principle, that innovation and efficiency from privatisation trumps out. Labour assumes, also as an ideological principle, that privatisation means the profits companies make must be excessive and it must be costing more than doing things in-house. Neither side seems interested in doing research and trying to find out whether or not privatisation does give greater benefits than costs or not (My suspicion is that the answer will usually depend on exactly what is being contracted out). And all the while, everyone seems unwilling to tackle the thing that really needs sorting if we have a long term sustainable health service: A serious discussion of what should and should not be free at point of use, how those free things should be funded, and (if through taxation) how high taxes should be to pay for it all.