want more state school pupils to go to top universities? Good. So does everybody. Guess what - you can help! How? Simple.
You're a member of the government. So, how about you, as a member of the government, get that government to put the money back for the school buildings programme, stop underpaying teachers who work in the state sector (maybe you could pay them as much as they can earn in the private sector? That might help), stop underfunding state schools whilst blathering on about how important it is that Toby Young become a headmaster, stop thinking that 'marketisation' (which shouldn't be a concept because it shouldn't be a word) is in any way a valid model for things like education (parents generally don't want a choice of 20 schools, they want one. A good one), and stop going on about this fantasy demon university lecturer who cruelly spurns state school pupils because s/he's bad to the core - these people don't actually exist, politicians just make them up so they don't have to put their hands up to the systematic undermining of state education by government after government for quite some time now.
How about you remember that books and computers cost money, which makes learning once you're back at home expensive, and look into not taking away the EMA? Think about the fact that, as books and computers are expensive, sometimes people like to go to places which have them already, and read the books there, or borrow for them a while, or do online research in peace; maybe then you could help keep open some of those library thingies that may well be the only place where state school pupils can get hold of expensive specialist books that are ten a penny in private schools, or get decent internet access in a quiet environment.
Oh, and maybe stop giving out this image that Russell Group universities hate people who went to state school. Because that might put people who went to state school off applying to Russell Group universities. And universities can only actually give places to the people who've applied to them. That's sort of how it works.
Cos thing is, people who care about what sort of school you went to don't tend to become university lecturers. They tend to become things like Prime Minister, and Mayor of London (ask the Chancellor for his university nickname if you don't believe me). The sort of people who become university lecturers want to teach people who are bright and engaged. They don't actually care about anything else. If you ask, they're probably as annoyed as you are that they don't get more applicants from state schools. So perhaps you could look into doing a few things that might actually change that.
Here's a piece from the Guardian giving details of what Simon Hughes said.