No estate, interest, or right of a profitable or beneficial nature in, over, or affecting an open space or burial ground shall, except with the consent of the person entitled thereto, be taken away or injuriously affected by anything done under this Act without compensation being made for the same; and such compensation shall be paid by the local authority by whom the estate, interest, or right is taken away or injuriously affected, and shall, in case of difference, be ascertained and provided in the same manner as if the same were compensation for lands purchased and taken otherwise than by agreement or injuriously affected under the Lands Clauses Acts.