This from a police training manual.
"The Highways Act 1980, s 161 provides that a person is guilty of an offence if, without lawful authority or excuse, he discharges any firearm within 50 feet from the centre of any highway which consists of or comprises a carriageway, and in consequence thereof a user of the highway is injured, interrupted or endangered. It is important to remember that the discharge is not prohibited in itself. It must also be proved that an injury to someone, or that someone’s passage was interrupted or interfered with (for example being forced to make a detour) or that someone was endangered, i.e., put in danger of injury. ‘Highway’ for the purposes of this section is restricted to a public right of way for the passage of vehicles; consequently it does not include footpaths, cycle tracks, bridleways, or cattle tracks.
The offence is not committed if the person discharging the firearm has a lawful authority or excuse for doing so, as where the discharge occurred during a clay pigeon shoot which involved shooting down the field and away from the highway."
Also worth noting that footpaths are owned by the landowner, so if you have permission to be there by the owner you can carry a firearm. If you haven't got permission think you can be done with armed trespass. Also a firearm (inc air rifle) is classed as laoded if the mag has rounds in it, even if the mags in your pocket.
Jon