When you appeal, you have to say why the school you want is more suitable, and why the school they have been allocated doesn't meet their needs.
Most kids in the UK don't walk to school at 6 and 8 (not being judgmental, most kids don't these days)
Most people round me use a pre school /post school childminder for this sort of problem.
Thankfully the school mine goes to has a pre school club
sympathy for your situation, it is a devil!