Please don't be influenced by discouraging comments, Secretsquirrel. The kind of scheme mentioned by ancientand modern above, encouraging state sector teachers to understand the process has been going on for years at Cambridge. Almost 20 years ago, I was a beneficiary who was invited to live as a Fellow and work on my own MA research in a Cambridge college and attend any lecture or seminar I liked, while being invited to lunch and formal hall or Fellows dinners by admissions tutors from nearly all the Colleges to learn about what they wanted and what we, as Sixth Form teachers, needed from them. (I suppose perhaps something could be read into the fact that a small number didn't invite me?!)
The tutors were keen that they should be approachable and were available on the end of a phone to discuss any possible candidate from our comprehensive. I was to spread the word in my areas/LEA.
As far as I understand, Cambridge put more money and research into this, earlier, but I doubt there is anything to choose these days. If you scrutinise the Sutton Trust figures, you can see which kinds of schools have successes at both Oxford and Cambridge as number of entries and success rates are recorded - by name for the most successful schools! (though not categorised by subject).
As has been said earlier, Oxford's pooling system is quicker and kinder. The Cambridge system is pretty agonising and could do with speeding up at least, but my understanding was that its original purpose was that the system should be as transparent as possible.
The point was also raised earlier that interviewing a high number of candidates might raise false hopes, and a stricter culling might be kinder in the long run. I was told informally the reason is that as many applicants as possible at least feel they have been properly considered and have had an opportunity to show what they can do, outside the exam system. I don't know if that is officially true.
And though sometimes young students can feel small and underconfident, it is largely to do with some of these stories they have heard and how they feel about themselves, though I think it is worth checking the entry stats for colleges and subjects, and success rate for state or maintained, male or female (available on the Cambridge Website, though not on Oxford's) in giving you a little help in choosing a College.