That's quite a thorny question, Dave. The law states:
Section 19 of the Firearms Act 1968 makes it an offence for someone to have with them a loaded shotgun, a loaded air weapon, or any other firearm (whether loaded or not) together with ammunition suitable for use in that firearm in a public place without lawful authority or reasonable excuse (the proof whereof lies on the person). The Anti-social Behaviour Act 2003 also extends the Firearms Act to include unloaded air weapons and imitation firearms.
BASC says:
The British Association for Shooting and Conservation has raised concerns with DEFRA, on behalf of its members, that allowing sections 19 and 47 of the Firearms Act to apply to all land mapped as ‘open access land’ might lead members of the public to misunderstand the scope of the provisions and contact the police. A possibility also exists that some members of the public opposed to shooting activities might make malicious complaints under section 19.
Section 47 of the Firearms Act makes provision for a constable to examine firearms and ammunition if he has cause to suspect a person of having a firearm, with or without ammunition, with him in a public place; or to be committing or about to commit, elsewhere than in a public place, an offence relevant to the purposes of the rest of Section 47.
From what I can make out, then, anyone with the proper certification can shoot on public land providing they take care not to kill or injure too many of the public (!). The existence of a Right of Way stresses specific prohibitions:
In England & Wales it is an offence without lawful authority or reasonable excuse to discharge any firearm within fifty feet of the centre of a highway which consists of or comprises a carriageway, and in consequence a user of the carriageway is injured, interrupted or endangered. [Section 161(2) of the Highways Act 1980 as amended]. It is important to remember that the discharge of a firearm is not prohibited in itself. It must also be proved that there was an injury, or that someone’s passage was interrupted or interfered with e.g. they have been forced to make a detour.
As with a lot of UK law, it's as clear as mud and this doesn't help:
Whilst the Firearms Act does not provide a statutory definition of what is meant by “lawful authority” or “reasonable excuse”. We believe that “lawful authority” would not necessarily apply to sportsmen as this seems to relate to those issued with firearms in connection with official duties such as police or military personnel. “Reasonable excuse” would apply to sportsmen shooting over land with permission. Section 19 of the Firearms Act with regard to having a ‘firearm in a public place’ also applies and is described on page 4. This legislation applies to all public places and not just open access land.
In terms of shooting on someone else's land without permission, that's not illegal, in fact, since civil trespass is not illegal under UK law. That's why it's not illegal to enter anyone's private garden.