Claims for payment of compensation under a tree preservation order by virtue of section 203, and claims for payment of compensation under section 204 by virtue of directions given in pursuance of such an order, shall be made to and paid by the local planning authority who made the order or, in the case of an order made by the Secretary of State, the authority named in the order; and the reference in section 204(2) to the authority exercising functions under the tree preservation order shall have effect subject to the provisions of this paragraph.