Just to reiterate what prh47bridge said.
In most cases, arguments about transport problems don't carry any weight at appeal - lots of people argue that their preferred school is on a bus route/closer to home/near a sibling's school etc and it isn't normally enough to prove 'prejudice'. But if you can provide evidence from your doctor to say that your child can't walk long distances, and can provide evidence of the walk that the offered school would entail, that will support your case. Whether it's enough to win, I can't speculate.
Also, have a look at the part of the School Admissions Code (available here) which mentions medical need and parents' and children's disability:
Social and medical need
2.27 If admission authorities propose to give higher priority to children for social or medical reasons they must ensure that in doing so they are not failing to comply with paragraph 2.16(g) of this Code, which prohibits the use of oversubscription criteria that discriminate against or disadvantage children because of their special educational needs or disabilities.
2.28 Admission authorities must not use this criterion to give a child a lower priority in obtaining a place at the school, but it is acceptable to give higher priority to children or families where there is a social or medical need (for example, where one or both parents or the child has a disability that may make travel to a school further away more difficult).
2.29 If using this criterion, admission authorities must give a clear explanation of what supporting evidence will be required ? for example a letter from a registered health professional such as a doctor or social worker ? and how this will be assessed objectively. Admission authorities? decisions must be consistent and based on this objective evidence. The supporting evidence should set out the particular reasons why the school in question is the most suitable and the difficulties that would be caused if the child had to attend another school. Admission authorities must not give higher priority to children under this criterion if the required documents have not been produced. (emphasis added)