My child has an EHC plan. Does this mean that they are automatically entitled to transport?

Not automatically. If children with EHC plans fall in one of the categories of eligible children (set out in the section on children of compulsory school age then they will be entitled to transport. If a child with an EHC plan lives within statutory walking distance, can reasonably be expected to walk to school on their own and does not fit within one of the other categories, they will not be entitled to free home to school transport.