"but he is operating within a government where the majority of the ideology and policies have been made by Etonians (or equivalent)"
As opposed to hypothetical governments led by Clegg (Westerminster) and Blair (Fettes)? The recent Prime Ministers with state educations are Brown (state grammar), John Major (state grammar) and Margaret Thatcher (state grammar). Amongst those who failed to become Prime Minster are Harriet Harman (St Pauls), Viscount Stansgate, sorry Anthony Wedgwood-Benn, sorry Tony Benn (Westminster), and Ed Balls (Nottingham High School, which he attended whilst his hypocrite father simultaneously campaigned for the abolition of grammar schools, so being a shit is obviously something he inherited from dad).
I seem to recall that in the nineties, the Labour front bench had a better class of public school than the Tory. Further back, a friend of mine was at grammar school with Shirley Williams' daughter, whilst Shirley was abolishing grammar schools for everyone else. And who can forget Diane Abbott and Ruth Kelly, both of whom talked loudly about state education for their constituents, but went private for their own children because they didn't think state schools were up to it. Kelly was education secretary at the time, and played the "as a mother" card, which was especially noxious.
If you want to find people who think that state education is a matter of little importance as they won't be using it as it's nqoc, Labour are at least as bad as the Tories. If you can find a Labour front-bencher whose child attends a state secondary school, let us know.