If within 28 days after such plans have been supplied to the Railways Board the Railways Board give notice to the appropriate authority that the Railways Board desire themselves to construct any part of the specified works forming part of Work No. 1 which, in the opinion of the engineer of the Railways Board, will or may affect the stability of railway property then, if the appropriate authority desire such part of the specified works to be constructed, the Railways Board shall construct it with all reasonable dispatch on behalf of, and to the reasonable satisfaction of, the appropriate authority in accordance with the plans approved or deemed to be approved or settled as aforesaid and under the supervision (if given) of the appropriate authority.