Joining in a bit late, and sorry for long post as educational inequality is something I feel extremely strongly about. Might be going a bit back to the start...
I'll nail my colours to the mast first. I went to school in a mining village in the 70s/80s. Most of the other children were from mining families and very few boys cared about education because they were destined to go down t'pit and why on earth did they need to learn stuff first? Parents thought the same so didn't encourage. Girls didn't care either because they expected to marry early and have their menfolk provide for them and the kids. Housing was mostly council.
I was one of the few odd ones out, but from a white collar LMC household one generation up from WC labourers thanks to my mum going to grammar school to 16 and dad being a natural mathematician (but with no exam self-confidence: he became a bookkeeping apprentice at 14). I got mercilessly bullied for wanting to learn, from junior school on. So by the time these kids were 7, they'd turned off. Jesuit maxim anyone? So I have seen what happens if nobody at home cares, first hand. My primary teachers were brilliant but couldn't help in all cases because everything they taught was negated by the constant "What do you want to do that for? Only swots do that." from the families. Swots were bad things.
Of course 10 years later, no more pits and cue a lot of unemployed men and women with no qualifications. Nobody knows what's round the corner but you can never take away education. I came out of the state comps with good A levels and a RG uni offer and a determination that any kids of mine would not have to fight the system if I could bloody help it.
So I would focus everything on reading and writing and numeracy at a very early age. But above all, making it relevant and fun and importantly, getting parents especially mothers involved as a group and as teacher for their own children. Keep classes small for YR, Y1 and Y2 and have a couple of teachers in them. 30 is too big. 20 or less. It's the one-to-one attention that helps most. All the parenting books for early years say it's talking to babies and toddlers that improves vocab and helps hugely. I want the UK to have positive learning culture, not a negative one. Smart = good.
I am sure that the kids who most need the help are the ones with the parents who also think it's a dead loss so don't encourage. Kids are naturally curious, they just don't need it knocking out of them.
I would not change private schools in any way. It would cripple the already overburdened state sector if a flood of children from parents struggling to pay fees were released by their bills going up 20%. If people want to pay taxes and also fees, that surely is saving the economy some considerable money. Also, I believe strongly that striving for the best (should!) produce people who will be capable of helping the country as a whole stay afloat. We shouldn't snipe at those who can as they can look after themselves: we should direct resources to help those who can't or don't have the chance. We need everyone, or things will get (more) unbalanced.
(deep breath... presses post...)