Agree - I got confused at first as you wrote "appeal" when there's nothing to appeal against as you haven't applied before.
Are you looking at boys, girls or coed schools? If you could specify it might be easier to help.
Whilst some of the private schools have places for those that move to Birmingham such as KES (http://www.kes.org.uk/admissions.html
), with the Grammars I believe you're in the same boat as everyone else. There will be children of various ages within Birmingham on the waiting list for in year entry in each of the schools and all will be sitting a test should a place become available.
My DD is in Camp Hill Girls, a few of her classmates have left and already been replaced by girls who have sat a test in year along with others on the waiting list. I know they have come from within Birmingham and I know of another girl who is being prepared for a test should a place come up. As far as I am aware another child is due to leave as well.
Unfortunately as this stage, there's the real possibility there won't be any available place for September in any Grammar as it's quite late in the year. If a definite plan is in place to come to Birmingham then you'll have to get on the lists ASAP as these things are sorted out quite quickly, within a few weeks. A girl who left at the end of the Spring Term has already had her place take up by someone else and we're only two weeks into the Summer Term.