It must be in the interests of those institutions to open their doors to the widest possible pool of talent. And of course Oxford, Cambridge and other institutions must look for potential in students from state school backgrounds as well as taking the ready-made products of the public school system.
But this is not as simple as it sounds. Friends of mine involved in the admissions process tell me in is very difficult to make these judgements -- how can you tell if a student who has relatively lower grades from a state school will turn out to be a better student than one with a string of As from the independent sector?
The Commons public accounts committee report published this week found that the government's drive to push up the numbers of students applying from the poorest backgrounds has resulted in marginal improvements. The report heaped most of the blame on schools, which failed to give students the right advice about applying, I'm sure this is a major part of the problem. There is a long-standing resistance in the state sector to encouraging pupils to apply for the top universities, where it is thought they will not fit in. The trouble is that this probably true. What a mess.
Ministers have disagreed with the report's findings, but they must know that there is a residual problem here that has proved hard to shift despite nearly 12 years of egalitarian New Labour intervention.
Meanwhile, the redoubtable Lynne Featherstone has unearthed an internal Cambridge University report on equal pay. This may go some way towards explaining why the university remains so resistant to change, despite the efforts of vice-chancellor Alison Richard.
Lynne writes: "There are some professions where change in pay and equal opportunities has been slow and a long time coming. I have a smidgen of sympathy for those where you have to have many years of service in order to get to the very top – and there is at least an argument that those years are needed to gain the necessary experience. The Law Lords might be a case in point.
But academia – despite its rather fusty image at times – is not one of those. Look at what happens to the youngest and brightest new academic stars – they are often snapped up and become professors at a young age. Decades of service are not needed."
The Lib Dem MP may have a slightly rosy view of how the academic meritocracy works, but she has a point about the evident injustice of the pay gap. As a result, she has reported the university to the Equality and Human Rights Commission. I will follow the story with interest.