A person who desires a highway to be stopped up or diverted but is not authorised to make an application for that purpose under section 116 above may request the highway authority or local authority who, by virtue of that section, are the appropriate authority in relation to the highway to make such an application ; and if the authority grant the request they may, as a condition of making the application, require him to make such provision for any costs to be incurred by them in connection with the matter as they deem reasonable.