I can't find anything which says how the list was compiled. It appears to be based on people's prejudice and further demonstrates the problem the state sector has in ever proving that it is at least as good as the private sector, if not better. The problem this creates is that those who are moving children from the private sector will be taking up places and creating an even bigger shortage than there is now.
When private schools become bankrupt, presumably they will then apply to become "free" schools, so the state may then fund some of the worst of the ex-private sector (it already is doing so). How much more sensible to stop this stupid competition between schools (except on the playing fields) and allow local authorities to plan on the basis of need for places.
Something should also be put in place to prevent those with money from renting property in the catchment areas of schools perceived to be successful in order to get a place, before moving back to their proper home. This is depriving genuine local people from accessing their local school.
The argument that "of course, you do the best for your own child" may sound reasonable but when put with "whilst trampling on other children" doesn't sound quite so good.