Sorry I have only skim read the last page or so. Of all the schools being mentioned, I believe LU has the most developed bursary programme. I think it's something like 25% receive something form of bursary.
I don't know if there are quotas at 11 plus for state / independent entry, but they must do something to gravitate towards a rough 50/50 balance - just as they must do to ensure reasonable boys and girls ratios in co-eds. I suppose a lot will depend on who actually takes the places up.
Where there are ratios is at university level and the bar from those from independent very selective schools (as well as very selective grammars such as Tiffin) is constantly rising. Please do bear this in mind! They are contextualised against their average cohort. Top grades from a comprehensive is usually enough for anywhere, but from SPGS, LU, G&L, KCS etc - they will need quite a lot "more."