The general presumption under common law is that the riparian owner of any ditches running alongside a public highway is the adjoining landowner and therefore it is that riparian owner who is responsible for maintenance of the ditch. This is a presumption that can be rebutted but the onus to do this lies on those asserting that another party is responsible for the ditch. The Highway Authority has the right to discharge water from the highway into these ditches but it is the riparian landowner who is responsible for maintaining them.
Normally, roadside ditches do not form part of the public highway as they are not available for the public to exercise their right to pass and re-pass along them (which is a requirement of a highway). The boundary of the highway would usually lie along the top of the bank/verge closest to the road. Additionally, a Highway Authority would not normally own the land on which a highway runs; the surface and as much of the soil below as is required for maintenance would be vested in the Authority but not the subsoil below.
An exception to the above may occur if the Highway Authority owns the land on which the ditch is located or if it has created or piped the ditch specifically under their highway powers. In these cases the Highway Authority can then become responsible for its maintenance.
A verge between a watercourse and the road would tend to be part of the highway and therefore the responsibility of the Highway Authority to maintain.