I think we are all agreed that all children deserve the right to a decent education, and that should be regardless of their parental income.
At the moment, a disproportionate amount of privately educated children get places at 'top' universities, not because they are more clever, but because they get the better results for GCSE and A level. Obviously some would get those results if they were not in the private sector, but many wouldn't.
Examinations have been dumbed down to the level where as long as you are a) reasonably bright b) do as you are told c) aren't in a disruptive environment etc etc then most children can expect to get an awful lot of As at GCSE. This is magnified x a lot in the private sector and that is what people pay for. It doesn't make them actually more intelligent though, it just makes them good at passing the exa
Top universities are now populated with frankly 'average' students and I imagine there are a fair few equally , or more so, intelligent children at crap state schools who don't stand a chance in hell of getting any of those places because they have been disadvantaged from the very, very start.
However, was probably twas ever thus, but I do think it has got worse in recent years, especially with the demise of the real and proper grammar school (ie where clever children got in without tutoring etc etc....boring myself now).