Air Weapons in the UK ARE firearms purely & simply because UK law says that they are.
Any "lethal" barrelled device is a Firearm in the UK under UK law, lethal being defined as propelling a projectile or shot with a force above 1 joule except for airsoft weapons (which have a specific legal definition) & which may be 2.5joules if single shot or 1.3joules if they fire 2 or more projectiles from a single pull of the trigger.
your examples above no gun-safe & no licence are simply exemptions granted to air weapons classed as "not especially dangerous" being less 12ftlb rifle, or less than 6ftlb pistol.
It does not exempt them from being firearms, it merely sub classifies them as "not especially dangerous" (air) firearms.