That the worst results are from rural areas, such as Norfolk, suggests funding may be part of the problem. Inner cities are likely to have greater funds directed their way. When there's funding an attention the lack of books or the lack of attitude in the home may be overcome.
Mind, in my young days, when we had the 11+, a great many of my classmates, in a direct grant school were sons of farm workers. They were the ones with the highest marks in that exam. But significantly, meeting their parents, it was often the case that the parents had been denied the education which they should have had; they were themselves keen readers and learners in later life. That suggested that an attitude would be present in the home which might not be present in others. I think it's that which still prevails; some parents just do not have the ability or attitude to serve their children well when it comes to learning. They never learnt or valued learning and their children don't.