We missed out on our eldest getting a place in our preferred Primary school a few years ago, she was 5th in the queue, we didn't appeal as we had no basis, we were out of the catchment but looking to move into it, we had family close by and my daughter had strong relationships from nursery school that fed into the school, though they don't recognise any this as a factor and it wouldn't make a difference to an appeal. There was so much swapping and changing that went on over the following months that we had a call in the last week of the summer holidays to say she was in.
Before you consider an appeal ask where you are in the queue, ask if it has moved at all since the release of the allocations and read thoroughly through the appeal criteria to see if you have any basis otherwise it is just a giant waste of everybody's time.
I could be wrong but I believe schools are not allowed to exceed the maximum class size for any reason other than for a child in care.
Good luck with it all and I hope it works out for you, it's horrible to not get the answer you're wanting.