cnaik - we were in your position about a year ago (? - no concept of time here!). I want to tell you that dd was allocated a place at a school that I wasn't happy with. I feel guilty writing that. Obviously, the school was full of children, and what am I saying, if I say that I didn't want my dd going there? But anyway, guilt or no, I couldn't face it.
Anyway, friends told us to just get her name on the waiting list of as many schools we liked (in borough, out of borough) as possible. This we did and sure enough, a place came up at one of them two weeks after the start of term. In fact, places came up at quite a few of them after the start of term.
As others have said, it is worth having a very good relationship with the admissions secretary. The secretary at the school she went to told us, over the summer, that a place was likely to come up, which allowed us to plan.
We did contact various appeals people (hence my having that number) but were fairly confident we didn't have grounds for an appeal.
Mainly, i want to give you my sympathy. It's not a great position to be in. I can remember how bad it felt.
Good luck.