With regards to her current school I agree with all the previous posts - approach the school, they should do something about it.
As for the Essex Grammar schools, at my DS's if any places become available then an exam sitting is arranged and any children who have expressed an interest are tested. I think this is the situation at all the Essex Grammar schools but you would need to ring the one you are interested in and ask. I don't think any will admit at this stage on past results. These exams have already happened at his school for next September's intake so it may be that year 9 would be the earliest transfer time but the school would be able to advise you best.
She is very bright and stands out a bit
. We looked at several Essex indies for my DD and they did vary alot in how selective academically they are - if the school are unable to solve the problem is there any other Indie option open to you?