Advice needed for a UK Primary School Admission problem. Please see below.?

First of all you have done everything right and it's quite appalling they still wont budge on the issue. By showing evidence on a map that you live withing the limits of their requirements there should be no argument on their end. I would try and find out what the issue is after you present to them the map and during your appeal ask one what grounds are they doing this. Good luck and don't give up...