Given that one can hardly trust the Daily Mail to report anything accurately
I had a quick look at the Quality Care Commission website http://www.cqc.org.uk
, as the source of this news story.
Picking a few hospitals in the highest risk band (band 1) at random, I had a look. A couple of them didn't appear to have anything at all currently noted against them, but were the subject of investigations and checks. Of those that did, some of the criticisms were about how information was reported (rather than the actual clinical care). So I think the 1 in 4 figure is perhaps rather inflated. Apart from anything else, some people being at risk in 1 in 4 hospitals is rather different from 1 in 4 people being at risk (which is what a casual reader of the Daily Mail headline might infer).
This is not to deny that there haven't been problems in the NHS - there have been several uncovered fairly recently, and clearly this needs to be addressed and dealt with. I gather that the QCC's new inspection regime is designed to do this - I'm not qualified to comment on whether it does or not, though at first sight it looks quite rigorous.
More directly addressing the OP, though, many of the problems in the NHS are put down by observers to the increased marketisation of healthcare, with hospitals becoming trusts and buying services of each other and so on. Many people decry the increase in the amount of management at the expense of health professional, especially nurses. But for example the lack of properly clean wards has been put down to the cleaners, who used to be directly employed by the NHS, being replaced by cheaper private companies providing this service, and them doing the minimum possible rather than a good job (in the name of efficiency).
So it seems to me that as the NHS hopsitals has become more like a private company, the care of patients has got worse, rather than this being a failure due to medicine being socialised.
Also relevant in the UK is that private hospitals (there are a few) take only easy cases, anything difficult or expensive they pass on to the NHS. And indeed, if the private companies make a botch up of things, like the recent breast augmentation failures, the NHS has to deal with the fall out.
If anything, failures in hospitals, whether public or private, suggest the need for an independent and powerful inspection which can insist on high standards. In other words, you need the strong arm of the government to make sure healthcare is as good as possible, whether this is to prop up failures from laziness, inefficiency, money saving, or anything else.