I think that to be fair it's not necessarily inconsistent to argue for non-selective schools but selective Universities (though I'm biased there as that's the position I hold myself). Schools operate at a sufficiently lower level that it should be and is usually possible to provide work differentiation through setting/streaming within the school. I think there's a lot of value in mixed schooling if only to remind people of the range of skills and people that exist in the world and that most of them are actually necessary. High-end universities are very much a bubble of future academics, leaders, politicians, etc, and seeing some people there who've been in a similar bubble since their age was in single digits... it doesn't do them any good, put it that way.
Rob: I'm also very pro having an elite Russell Group/Oxbridge, I think that's absolutely the appropriate age for people in all fields of life to start really being able to focus on what will make them brilliant at what they do. On the other hand, I'm quite sympathetic to the view that there are less bright private school pupils who are going to Oxbridge instead of state school pupils, because private schools are better at playing the exams game. And exams can be taught and played as a game - something I know well, from having had to teach myself how to play - without necessarily providing an education that will mean better success at Oxbridge.
That said, I accept that basically we have to use the metrics that are available for state school entry - and one of the main issues with state school entrants is applications as much as/more than results, too many state pupils have the grades but don't apply. I don't think Oxbridge are the main people at fault for their selection biases/issues by any means, and I agree that it's sixth form level where the targeting needs to happen.
Also, since we're doing this:
Primary school - Local village school, Church of England
Secondary school & Sixth Form - Local Comprehensive in nearest town
Degree - Cambridge