pokhara, what you need to do is this:
Phone the council, and ask for details of how to appeal.
Ask them for their criteria. If they say 'physical disability', look on the NAS website for the case law that accepts ASD as a physical arrestment of brain development.
Talk to someone in authority, and explain that as ASD is physical and it is the ASD that causes your DS's difficulties with walking, that by deduction, your DS's difficulties are caused by a physical problem.
Follow procedure and write a letter of appeal, stating the case law and that as your DS has a physical condition of the brain, which directly affects his ability to walk, you trust that they will be happy to accept that he meets the criteria, and therefore, you are requesting that they provide you with a blue badge asap.
I have a copy of the letter I did somewhere, if that helps.
I am on Page 3 of the DLA Mobility question, trying to qualify for High Rate Mobility.