mrz has a point here.
in fact in UK there are very few very poor people. They are just poorer than others, but not absolutely poor, homeless, starving. Most people have internet, tv, food, clothes, place over the roof, books, and prospects. All have access to libraries and education centers.
Its hence not necessarily the issue of wealth. I said before that at my sons DS the poorer people usually invest more time into their kids, as they realise that grammar is the only way for them. Richer parents have a back-up plan. Its not wealth related.
The problem, amongst others, might be, that there is no culture of parents actually sitting with kids, checking homework, relying too much on school reports, progress, and assurances that the school does what is best for your child.
This is not dependent on wealth, but on attitude. Middle classes fall victim to it too, as do indeed upper classes, as even on this forum some mothers said that "private schools are good for you as they claim to find the right place for your child in secondary school, suited for your child".
Its foolish to rely on private school to tell you that your child is not bright enough for Westminster School - as its likely that the children who are, are indeed receiving extra tuition at home anyway (despite being at private prep schools).
Perhaps to improve the system, you need to start of with the young ones, and with educating their parents too, so that they do find time to sit and do homework, to order bond books, to investigate if there are grammar schools, and what one needs to do to get in (just enter MumsNet.com).
If that would be the case, then perhpaps you could delay the need for grammar schools till GCSCEs, which we could say is the universal required education level in this country. Afterwards kids could go various ways.
Its a complex issue. Also nobody said that grammars and good comps cannot co-exist.