It's not politically possible to sell it off wholesale, which is why they have adopted the approach of creeping privatisation, requiring elements to be tendered and awarding contracts to private firms, while keeping the main NHS underfunded, overstretched and demotivated, in order to reduce the public support it has and weaken opposition to further privatisation.
This for example shows the pace it's happening at.
Leading Tories are on record as wanting to privatise it - for example, both Letwin and Hunt have written pamphlets arguing for that. It's not yet possible for that to be formal tory policy.
When they are plainly working towards that incrementally, I hardly think that the claim that they want to open it up further to private firms needs any more substantiation.