I never venture into anything political on TSR, but nexttime's and Reality Check's perceptive comments lead me to chime in...
There is no doubt a problem with perceptions of Oxford in some sections of society. Children who would be interested in and benefit from an Oxford education are told that Oxford's 'full of snobs' or 'not for the likes of you'. There is plenty of work to do in changing those attitudes, and it won't be easily or quickly done.
A separate problem is the idea that a university education is something that everyone ought to aspire to 'in theory', and that those who are not sufficiently academically gifted to go to university are somehow a lower stratum of society that those who are. This is obviously wrong not only because our value as people cannot be judged on our intellectual capacities, but also because, as the above posters point out, the ways of living a fulfilling life are infinitely various, and it's blinkered in the extreme to think that a university education is a sine qua non of the most successful life.
What I want to add specifically to what has been said already, though, is that the elitist attitude outlined in the above paragraph has over the last twenty years been bolstered by a more insidious (because less obviously misguided) elitism that originated (I think) in the Blair government. That was the idea that we ought to send more and more people to university not because (as was and no doubt still is the case) there are lots of people out there sufficiently equipped to do well at it and who would benefit from it, but because academic training is somehow intrinsically superior to vocational training. This was the idea behind turning away from vocational training, or wherever possible turning it into (pseudo-)academic training. This grew out of a fear of elitism, but is in fact an elitism in its own right. What that regime should have tried to stress was that there is nothing inherently more valuable about any kind of training - or, for that matter, any kind of job, be it academic, clerical, manual etc. - than any other.