Advice needed on independent schools and the local authority

I have been looking for a secondary school for my son to attend as he is nearing the end of his primary school.  The school I feel is the most suitable for him is an independent school, however these schools are much more expensive for the local authority to fund.

I am going to have to fight to get hima place so what I am asking for is advice from anyone who has been through this before, and what sort of examples did you give to the local authority to prove that the independent school was the best school for your child.

I already have a few examples but your advice or suggestions would be greatly appreciated.

Thank you