Can a parent come to the UK with a child on a Child Student visa?

The Child Student visa itself does not let dependants come along, but there is a separate Parent of a Child Student visa.

That parent route is restricted: it is only available where the child is between 4 and 11 years old and attending an independent school in the UK. Only one parent can be in the UK on this route at a time, and it does not allow the parent to work. For older children, parents generally cannot accompany them under this scheme.