My advice would be to apply anyway, for deferred entry if you want. With AABB predictions and your GCSEs it'd be an uphill struggle, you'd have to impress at interview and in other areas, but it's by no means impossible. You've got nothing to lose, and Oxbridge wont discriminate against you if you're rejected and decide to reapply post A level. If nothing else, applying this year would be a valuable learning experience. There's not a lot of point wasting the opportunity this year, unless your school's really going to make your life hell for doing so.
About that, the idea that your school would prevent you from applying is frankly ridiculous, it is your application. If necessary it's quite easy to apply independently if your school refuses to budge, though it's advisable to stay on the good side of whoever's writing your references.
Also, it sounds obvious, but do make an effort to get your ASs up to AAAA. It's not absolutely necessary (I got AAABBC) but it'll certainly help and might encourage your school to raise your A2 predictions. It really ought to be at least an achievable goal if you are of the right standard and knuckle down. Don't overload yourself with resits either though.
Lastly, about needing to be an all-rounder, I have to disagree with your school again. I applied for maths (twice) and I got a strong impression that they really didnt care about anything else. I know I'm pretty terrible at anything that doesnt involve pushing greek letters around a page. I would guess that they like to see evidence that you can work hard, handle pressure, and are generally pretty bright, but that's as far as I'd go.
Sorry for the ranty tone of this post. It annoys me when people are put off by their own schools, the people who should be helping and encouraging them. I'm not normally this bitter