I think MrsMipps point about not really having the potential to be a great footballer at 18 if you've never kicked a ball until then is interesting. I suspect there is an element of 'use it or lose it' with brain development in the formative years, although probably you need a fairly severe case of not using it to suffer irreparably.
I think that a child that has been very poorly educated to the extent where they have given up fairly early on, really won't be able to catch up by the time they are 18 whatever their initial potential may have been. While this really wouldn't apply to the 3Bs candidate from a low achieving comp. who clearly still does have the potential to succeed at tertiary education, I think it may apply to some of those with much lower grades and could be one factor that skews the statistics away from state children going into higher ed.
Another thing that I'm sure skews the figures towards the privately educated but which isn't really to do with the quality of their education is the fact that almost by definition they all have parents who care substantially about their education,and so will have very supportive homes and high aspirations. This is one of the contributing factors to the harder working ethos at private schools and also means that these children would likely do pretty well (maybe not as well, but who knows?) in a state school had they been there instead, but it's an effect that is virtually impossible to quantify. (Note I am not that state children's parents can't be like this - many are, but in addition there will be many who aren't so much).
It's really difficult to say how much of the better grades achieved by private schools is down to better teaching/smaller classes and possibly a slightly brighter intake as against how much is down to harder work, pushier parents and higher aspirations, so it's extremely difficult to know if and how much how much positive bias should be applied to state applicants (and if it is, how you eradicate other inequalities that arise), but it is right that the questions are asked and effort is made somehow to address disadvantage. Personally I prefer schemes that address the problem at the cause - ie raise standards in schools so that all children can achieve their potential at school but there is a place for access schemes to allow for lower offers to disadvantaged children too. I'm not sure about the funding thing though - my gut feeling says if it costs the same to educate any child at university then the university should receive the same level of finance for all and the government shouldn't use this as a stick to encourage wider access.