Under common law, pedestrians, horse riders and carriage drivers have public user rights over the whole width of land designated a highway. Usually this is between the hedges and fences on either side of the carriageway and this area may include verges. These rights may, however, be restricted where limitations are imposed such as the provision of a footway, along which only pedestrians have user rights. This and other legal requirements effectively limit the width for vehicular users to the made-up carriageway, what we call the road.
Horse riders can lawfully cross a footway, say at a road junction or verge-crossing, and ride along the verge at the back of a footway if it exists. There are exceptions to this, however; for example, if a Traffic Regulation Order or local bylaw exists specifically forbidding horse riders the use of the verge. You would know of such an Order by the display of signs indicating the ban.