Welcome to the forum, and thank you for your email which I have seen.
I can confirm that this is a state school, and that there will be an independent panel set up to consider appeals against refusal to admit.
Although you can ask the panel to consider whether the admission arrangements were lawful and have been correctly applied, I suspect the chances of your getting a place as a result are approximately zero, not least because of the number of other children involved. (An appeal panel is not going to allow more appeals than it thinks the school could cope with.)
Have you read our guidance on appeals? - See ToadMum's link above.
Have you seen how to present a well-balanced case?
https://www.elevenplusexams.co.uk/appeals/general#a43See also "C21. How not to win an oversubscription appeal!"
and "B12. Any do’s and don’ts for an appeal against non-qualification?"
Quote:
b) Don’t spend time saying how wonderful your child is at extracurricular activities unless the panel ask you a specific question. Even if they do, don’t expect non-academic extracurricular activities to influence a panel’s decision.https://www.elevenplusexams.co.uk/appea ... cation#b12