I think one way, when you are in a position of employing others, is to employ people like you, then promote etc. You can vote for political parties that try and address this (albeit in a limited way), or have some of their leaders from working class backgrounds.
I like your teeny weeny start, Hully. Tbh, I think academies are neither here nor there. But private schools make a very big contribution.
Boy from round my way got into Eton the other day. I hope he doesn't forget his roots and does his best for other disadvantaged kids instead of becoming just like all the other old Etonians.