I have no idea what the current situation is for prospective university students (do they still have fees? can you get grants again?), but back when I was a student, poor kids could win scholarships to even the very best public schools through the Assisted Places Scheme. Then they could get free university places thanks to student grants. Both of these were abolished by Tony Blair within months of gaining power. Labour did not want an educated working class, possibly because it would diminish their share of the vote. Then they went even further and made students pay fees for university as well. It's no wonder really that in the years since the balance has shifted towards university being for rich posh privately educated kids again.
Ahhhh Labour......The Peoples Party™