I can understand the rationale behing H&E's suggestion, but as usual, although I don't think we have wildly different political philosophies, I will of course disagree!
The point that the universities are underfunded in comparison with the States is a fair one, however, to my mind at least, one of the best things about Oxbridge lies exactly in this distinction: Oxbridge is an academic institution, and only that, it selects students purely on the basis of academic merit and potential. This is the argument the university uses time and time when trying to defend the cultural biases inherent in its student body, and to resist interference from London and the imposition of a quota system. If Oxbridge reneges on this principle to benefit rich people, it would have a very hard time defending itself against the quota system etc, to say nothing about the public outcry and bad press which i think we can all agree are the last things the ivory towers need! The idea, although interesting, is practically and politically impossible, and although some people may agree with it, there will be far too many opponents of such a step for it ever to be fully implemented.
However, there is another very obvious solution to this dilemma: raise tuition fees! At present the aforementioned rich kid* only pays at the most 17% of his education. Why not make those with incomes over 150,000 pay the full shebang, those with 149,999-85,000 pay 60%, etc etc., leaving probably substantially more money at the government's/universities' disposal. Obviously not a very popular idea among middle class families and students, who deserted Labour in droves at the last election (e.g. Cambridge, Bristol West, etc.), so perhaps not a political probability for a while. We shouldn't however, that the vast majority only protest vote once on the same issue.
* Isn't it telling that in all the hypotheticals, everyone assumes the rich kid had a rich dad?