You're basing your observations on a very limited sample size, the only way we'll know for certain if there's been any kind of shift (which I doubt very much) in terms of the state/private divide is when the statistics are released. Most Oxbridge applicants are predicted at least 2A*s at A Level and have a string of A*s at GCSE and As at AS, and Oxbridge do not care if you've got leadership positions in your school so both of these are more or less irrelevant. And the fact of the matter is that it's impossible to predict who will get into Oxbridge and who won't. Your staff might be good at guessing but they're (obviously) not 'never wrong'.
There's more to the Oxbridge admissions process than above. Firstly, they're not just looking for the people who are the brightest on paper. It helps, but what they're really looking for is people who are very good at dealing with unfamiliar material, can think on their feet and would be able to learn well in the tutorial environment. It's very unusual for someone with ABCD at AS to get an offer (are you certain that's true and if it is, there's probably extenuating circumstances) but the fact is that high grades are not enough. Interview technique also definitely isn't enough; there was recently an article in the Guardian by an admissions tutor who said that all of the technique students from private school learn for interviews are completely transparent. The point I'm trying to make is that they're not just looking for the applicants who are best on paper. There are lots of other attributes they are looking for (including, to a certain extent, being the kind of pupil the tutor personally would like to work with over the next few years, it's not just about academic attributes) that could cause that discrepancy. And if you usually get 3 or 4 Oxbridge students per year then it's no surprise that occasionally you get anomalously low years. We normally send around 3 students to Oxford and this year we got 5 - anomalies happen.
Oxbridge definitely do have a bias against Independent schools but even with that bias, privately educated students are still massively overrepresented at Oxbridge (there are more than six times the number of privately educated pupils in Oxford than there would be if the intake reflected the proportions of privately educated pupils in the country), so it definitely is not the case that you can't get into Oxbridge if you're privately educated. You're still much more likely to get in than the average state school pupil. These biases exist for a good reason, it's not "politics", it's a simple fact that Oxbridge are looking for potential rather than achievement. You get a much better education at private schools so they're going to help you to reach your full potential. As a result, it is quite possible that for two pupils - one state, one private - with the same grade set, the state educated pupil has a better academic potential because they've managed to achieve this grade set despite the barriers to their education. That's obviously massively simplified but it's a point that's generally fair. Critically, I think there's a misconception that Oxbridge have a bias against privately educated pupils in order to make their statistics look better. This is definitely not the case (at least, it's not the main reason). The main reason is that their data shows that having this bias ultimately improves the quality of their pupil intake.
So in conclusion, Oxbridge have a bias against the Independent sector but I believe this bias is fair as it helps them get the candidates with the best potential rather than the best achievements. I'm very sorry that you didn't get in this year (and about the situation in your school in general) but blips happen. I go to a comprehensive school and this year, well over half of the pupils who applied to Oxford got in, much more than usual. What we need to see is the national trend rather than basing opinions on small data sets.