Well for a start, you could shoot Gordon Brown and the rest of the Labour Party class warrior brigade who trash outstanding British educational establishments to get votes before sending their kids to private tutors, top grammar schools and American Ivy League universities, all the while undermining the prospects of the very people they're supposedly fighting for. While you're at it, burn down the offices of all tabloid newspapers, who take joy in making Oxbridge students out as a bunch of scandal ridden toffs. For example, May Day stories never mention the people jumping off the bridge aren't Oxford students - last year it was 33/34 non-Oxford, this year not a single one was from Oxford.
Once we've done that, well...
Information is the key. Spread out as much information, in as many media as possible. We provide detail stuff online, we print prospectuses, we run open days, we invite people over for conferences, we send people thousands of pages of literature free, we pay for people's room and board in Oxford, there are even Summer Schools which will pay for you to experience studying in Oxford. Oxford has made the change - the only problem is letting the world know about it.
Everyone cane make a difference. If you're from an under-representated background and come here, why not tell your local newspaper? Dispell the myth - it'll make such a difference! Even if you don't, go back to your school and talk to U6th students, offer to help with applications, give advice, give them assurance. It's the sort of grass roots, trustworthy information which will cause the real change in perceptions.