No, and indeed children of well educated well off people generally turn out that way themselves, the opposite for the poor. One might well argue that education should be on the merits, and not be decide on whether daddy is able to pay the tuition for the university with a name that guarantees a higher level of access. If your parents are poor and uneducated you are already up against it, not having well functioning support network.
I generally support the notion of trying to level the field as much as possible. The actual problem here is that England is broke, not that you want to discriminate more than you already do, but the effect is much the same.