Quotas will do nothing to solve this problem; what is needed is a culture which does not put media circulation (which is easy to increase by fuelling confirmation biases) ahead of the very people in whose interests those attacking Oxbridge claim to act. However, such cultural shifts are far harder to achieve than the arbitrary imposition of a quota - an option which may be easy but is most certainly not right.
The job of chairman of the BBC Trust is up for grabs. On paper it looks like a dream job. Not too taxing; perks of being a civil servant; good pay; great working environment; interesting, high-profile, semi-altruistic organisation. However, unless you've been living on Mars for the last 15 years, you'll know that this is, in fact, the job from hell.