It is not a specific offence to shoot across or near a public right of way, but it could be classed potentially as a common law nuisance, wilful obstruction of a highway under the Highways Act 1980 section 137 or intimidation.
Good shooting practice requires that consideration should always be given to other users of the countryside. Although it is not a specific offence to shoot across a right of way, it is an offence to disrupt user of that way and cause a nuisance. It is suggested that shooting should halt whilst people use nearby rights of way, and that it is ensured that users have left the area before resuming. This is a necessary safety precaution and it should avoid causing an excessive noise disturbance.
Highway authorities (i.e. a county council or unitary authority) are responsible for asserting the rights of the public to the use and enjoyment of rights of way, as well as maintaining them and keeping them free from obstruction. Anything that impedes the existing legal access to a right of way may be an obstruction. And the obstruction of the highway constitutes one form of public nuisance.
When reporting to the highway authority you should give full details of the exact circumstances of the matter complained of; the nature of the obstruction (e.g. a shoot taking place across a path which you feel you cannot pass safely), its exact location, preferably with a grid reference, and (if known) the path’s number. The date and time when the obstruction was met; the names and addresses of any witnesses; and, if known the names and address of the landowner should also be given. You should also consider reporting the matter to the police.