I'm a Cambridge graduate and as a young child received free school meals when my dad went through a period of unemployment - even when he returned to work he was a low earner and I received a full grant when I went to uni (back in the good old days when there were grants)
I went to a distinctly average comp, followed by a very good 6th form - my wonderful Headteacher at that school, plus my amazing parents (and being born with a brain which retains info easily) are the reasons I got in.
I wanted to go to Cambridge from when I was 13 or so, most of my teachers told me not to bother
. At my comp, going to uni was rare, Oxbridge unheard of. Most schools locally were similar.
On the grammar school point, I've always been a fan. I thought grammar schools were the answer. I now live in a grammar area (Bexley) and can see first hand how crap the system is. My eldest DS was top of his class all through primary (his is an 'outstanding' primary so of good standard you would think). He had no tuition for the 11plus and failed. Every child in his school who passed was extensively tutored. As were the children from his football team, who attend the local private prep school. State schools in our area say they are unable to coach for the 11plus as it is outside the national curriculum. so much for a level playing field.
The 11 plus nowadays doesnt pick out the brightest children. The ones who get the best marks are those who are coached. I doubt I would have passed. the alternative comp which my son attends is frankly crap, with 30something percent of A-C grades at GCSE (compared to 100% at the grammar). The students in the top sets are unmotivated and ignored - the focus of the school goes on the 60% not achieving A-C passes...I think this is pretty typical of average comps nowadays, its all about the bottom line, and improving your lowest results. As things stand, I expect the percentages of state school non grammar Oxbridge graduates will continue to fall.