Depending on your childs age you need to make it clear that he needs a lot more supervision when walking than other children his age.
I've found this and you may find it helpful.
How do I qualify for the lower mobility rate?
To qualify you must show that your child usually needs help when walking in unfamiliar areas. In other words, without the help and guidance of another person, s/he could not make real use of her/his ability to walk, except along familiar routes.
You must also show that your child could benefit from 'enhanced facilities for locomotion' such as a car or taxi. Put simply, you must show that with the help of 'enhanced facilities' your child could be mobile and that s/he would benefit as a result, eg s/he would enjoy increased social contact.
Explain on the application form why having these opportunities will help your child (eg because they have under-developed social skills and need as many opportunities as possible to integrate into the wider community). Use the application form to explain why your child cannot use public transport.
I found thishere
I hope this helps, sorry I've got to go out soon. Good luck xx