The BBC has recently featured articles on the narrow social elite dominating British politics and music. The former particularly annoyed me, because it started out noting the trend for posh public school boys to dominate the top jobs - even noting Howard Wilson (grammar school boy and alumnus of Jesus College, Oxford) had seemed like an end to such public school domination. Around half way through, however, it suddenly switches its attention to Oxbridge.
While it's true that Oxbridge has a disproportionate number of public school students, that's largely attributable to application and qualification rates. Oxbridge entry is by academic merit - as this BBC piece highlights - and, in my experience, there's certainly no bias in favour of those from posh backgrounds. You can't simply buy your way in to Oxbridge and it doesn't (currently at least) cost more than most other universities. Thus, Oxbridge is more analogous to grammar schools than public schools.
It seems that the original BBC article misleading conflates a social (class) elite with meritocratic intellectual elite. I'd certainly hope that the politicians running the country are some of the smartest people around and, as such, it doesn't surprise me if many of them went to Oxbridge (any more than that a presumably disproportionate number are graduates). I'd be far less welcoming to rule by a narrow social elite, both because of worries about class-biased legislation and the likely implication than some of our smartest potential politicians were being denied the potential to contribute because of the accident of their lowly birth.