Make sure you get both documents - Appeal Code of Practice and Admission Code of Practice.
The LEA will, in my experience, be putting a very technical argument based on the fact that there are X number of free places "in the borough" and that they only have to educate your child "within the borough", not at the school of your choice. At our appeal the LEA seemed very dispassionate and uninterested.
The head, and/or head of governors, from the school you want to get into will also be there and it is up to them to put the case why your child should not be admitted into that particular school. For Key Stage 1 this will inevitably be the 30 pupils/ not enough space argument.
Here's another thing. Find out - I think the LEA/Primary Admissions must tell you - what the exact numbers are in the school overall. It may be that Key Stage 1 is down a couple, e.g. that while there are 30 in reception there are only 29 in Y1 and 28 in Y2, say. This will be to your advantage because you can then argue that they are not at capacity.
Have I mentioned the Advisory Centre for Education yet? They are an independent body and will advise you for free. They are very good - phone them. They don't have magic answers but they will tell you exactly what you should be finding out and, most importantly, what questions you should be ready to ask the school at the appeal panel! their site is here.