For goodness sake, trisher. There are hundreds of appeals every week and almost every single one fails. There is an official School Appeals Code and, as far I can tell, the appeal panel followed it. This is nothing to do with human rights. The LA is providing an education and would almost certainly provide transport to the nearest school with places. If gillybob felt she was dealt with discourteously, she should complain, but it won't make any difference to the outcome.
School admissions and appeals codes are there to protect the rights of the applicants as well as the other pupils already in the school. Gone are the days when heads and LAs could keep places in reserve for children moving into the area. The illusion of school choice put paid to that, because schools are obliged to fill all their places up to their Published Admission Number.