Thanks to you all for the response and encouragement everyone. In no particular order:
(i) I applied for History, but I'd rather not say which college as it might identify the admissions tutor (who was very helpful / supportive afterwards). It was an older college.
(ii) The fact that there is a quota for private schools does NOT mean that there is one for state schools: the quota for private schools is a certain maximum. There is no max for state schools, only a min that corresponds to the complement of the private school max.
(iii) The school received a report afterwards which made absolutely no reference to any quota, I have to say, but didn't fault my application in any respect. Consequently, the school contacted the college and that's what led (eventually) to the talk with the tutor. The implication was that the college (rather than the university) had an imposed or self-imposed max for private school applicants, and had (slightly) exceeded that limit in the previous years. I am firmly of the opinion that colleges make adjustments over a three-year rolling average (if you see what I mean) so that their figures don't exceed a quota.
(iv) Taking my experience into account, I would advocate a blind points system for each subject for each university. I believe they have something like it in the south of Ireland. It would mean going to a general, broad, bacc-style exam - 6 subjects say - so awarding points out of 600. The market would then determine the threshold for each subject for each university, based on the UCAS applications. Law at Oxbridge might be 570; Law at Nottingham might be 500; etc.
(v) I am not in favour of 'positive' discrimination; as someone from an upper working class background, and female, I can do without being patronised; I'll get there on my own bat or not at all.
(vi) My school reported the matter to the TES - against my wishes - but they weren't interested.
(vii) I'm looking forward to getting into Oxbridge because I believe (honestly) that admissions aside, if one can do the business there, they do NOT care about gender / race / creed / background. ROLL ON NEXT YEAR!