I agree that it is absolutely necessary to start much earlier - there is no point expecting ANY university to even up the differences in education at age 17/18. That's not what it's there for.
But I still think - idealistic as that may be - that good, inspirational and most importantly aspirational teaching in the Infant and Early Years setting would do more to even things out than anything else. Naturally, this needs backed up by some hard, practical and therefore expensive and difficult changes. So, idealism shining brightly:
Let's start with a "Homework" club after school for those who don't have a quiet place to work, incorporating enough teachers/TAs/parent helpers/volunteers to listen to every child in there read - every day or other day. Same with maths - basics, repeated, like Kumon. The basics need to be second nature - however it gets into small heads, it needs to be repeated and reinforced. Songs, rhymes, timed table squares, repetition - whatever works.
Teachers who are free to teach, not deal with basic socialisation, would also help. Perhaps a breakfast club would be able to assist with some of the socialisation, whether that be the use of cutlery, basic table manners or just pleasant conversation, at an appropriate level.
Proper chances for running round in the playground, especially for boys. Keeping in should be an absolute last resort punishment in primary school - energy needs got rid of!
But absolutely none of this is any use unless teachers help their pupils to aspire. Nothing annoys me more than hearing or reading the phrase "it's not relevant to [them]. The "it" in question is usually some piece of knowledge that older and/or educated people would regard as fundamental - not because it is critical to surviving day-to-day but because it shows that you have thought beyond the basic, you have some shared history/culture/knowledge, you'll understand the references, just a bit more "You're one of us". Note I am not condoning any sort of "old boys'/girls' network" but what I am saying is that it gives a connection. Phrases from Shakespeare, the King James or Good News Bibles, the great poems (ancient and modern) are bound up in the language. If these are dismissed as "not relevant" then we lose something. Perhaps we lose the ability to appreciate and use expressive language, or precise language. Perhaps our vocabulary becomes restricted - and who would you prefer as a lawyer, a draftsman, an advertising copywriter - someone who could use language properly or someone who can just about manage textspeak? Why are we denying children the opportunity even to try?
I appreciate this is a polemic, and unlikely ever to happen. But going back to where I began, if there is no aspiration at home then it must come from school. To fail to expect the best is to fail the pupils.