I agree with jimjams, I think a lot of the problem is children from some schools - often state schools - either not being encouraged to apply, or, as was the case in my state comp, being encouraged but not doing so as they thought it wouldn't be their sort of place.
I did apply and get in, but I had 2 Oxbridge educated parents and various other family members who'd applied- in my family it was unusual not to apply, so I obviously wasn't a typical comp applicant. But other children from my school didn't apply who could have.
Also I think there is a problem with fitting in for some applicants from less privileged backgrounds. At our Oxford interviews, we had a mulled wine reception, whereas at other universities the applicants would have been taken to the pub for a beer. Oxbridge colleges do have a very different social scene to most other universities. Balls, Unions, lots of ski trips, many students who do have quite expensive expectations of how to socialise. I don't think that's changed very much since I was there. There are all sorts of social opportunities, and colleges vary in their habits, but it is distinctly different from other universities and I can quite see why not all 17 year olds are attracted to that. Some are intimidated, others just not wanting to buy into the atmosphere of privilege. I enjoyed my time at Oxford but it was totally different from my later experience at other universities, and not always better.