If the right of way in question is adpoted highway, then the highway authority will be responsible for its maintenance and will be liable to its users. The landowner merely retains his interest in the subsoil from which no liability should arise.
If however the right of way is not adopted, no claim for damages can be made. The House of Lords has confirmed that as a person using a public right of way does so by right he cannot be the visitor of the owner of the land over which the way passed for the purposes of the Occupiers Liability Act 1957 and that there is no liability in such a landowner in negligence for non-feasance in respect of injury caused by the condition of the way.
There appears to be no obligation on a landowner to maintain the highway nor any liability for injury caused.