There are two factors to prejudice. You have to convince the panel that the prejudice to the school by taking your child is less than the prejudice to your child if they don't get the place. However, if there are many children appealing, then you have to convince the panel that the prejudice to your child is greater than the prejudice to the other children. So, you need to make your case as good as you can.
Start by making sure no mistakes were made that stopped your child getting a place.
Then look at the numbers admitted in past years - have they had more than whatever the PAN is? That shows precedent - they've coped before, why can't they cope now?
Look at room sizes and facilities - they will say the rooms are too small, the corridors crowded, accidents will happen, etc. Are they? Have there been any accidents?
Look at what the school offers that other schools don't. Major on that.
Don't go down the 'my kid needs his friends' route unless you have evidence that your child is more vulnerable than other children. All kids want to be with their friends, but life isn't like that.
Don't talk about logistics, unless your child has a disability or condition that makes travel more difficult. All kids would be better near to home.