It's eerie how these types of attacks against Social Programs follow the same argumentative lines all around the world. In Brazil we have a Universal Healthcare System that is based on UK's NHS and our reactionary media (a.k.a the entirety of our MSM) loves to attack it using these same types of arguments from British Tabloids: "If it's being badly handled we should cut the entire thing then!"
Our Healthcare System is in a pretty bad shape too. It failed to have good coverage in a lot of places (since we are a Continent sized country) and it's getting more precarious where it's already established. There's not enough Doctors, patients die in the corridors, it doesn't have medicine to everyone, there's lack of ambulances, the clinics are overcrowded and its public workers are not well paid.
Shutting it down will not solve anything, though. We can't just pray for the Invisible Hand of the Market coming in to replace the entire thing and supposedly be better at it. There's a greater responsibility here and we can't bargain with people's lives. It needs to have greater funds allocated to it and that's the end of the story.
And I suspect that's the same verdict for the UK or any place that has been hit by Austerity. Like that saying you anglophones have, we can't just throw the baby out with the bathwater...
