Law - Military.uk

Ammunition

The appropriate FAC is required to buy rifle and pistol ammunition.^[source]
The appropriate SGC is required to buy shotgun ammunition.^[source] Although a SGC is not required to possess normal (not slug) shotgun cartridges.^[source]
The following is designated "prohibited ammunition" and typically requires Section 5 authority. Ammunition or projectiles/missiles designed to be:^[source]
armour piercing
incendiary
explosive (on or just prior to impact)
expansive on impact and be designed for pistol (e.g. soft point & hollow point)
noxious
No licence is required for blank ammunition, as long as the diameter does not exceed 1 inch (e.g. up to and including .50 BMG).^[source]
No licence is required for inert ammunition.^{[source, page 14]}

A FAC is required to purchase a firearm that does not fall within the other sections of the Firearms Act 1968. This will typically include: bolt action rifles, straight pull rifles, semi-automatic rifles in .22 rim-fire, smooth-bore shotguns with magazine capacities greater than 2.
Buyer to be eighteen or older.^{[source & source]}

A SGC is required to purchase a shotgun (smooth-bored) with a barrel length of 24 inches or greater, and the bore not exceeding 2 inches in diameter, and no magazine or a magazine capable of holding a maximum of 2 cartridges.^{[source & source]}
Buyer to be eighteen or older.^{[source & source]}

Authority is required to purchase any of the following:^[source]
automatic firearm
semi-automatic rifle (other than .22 rim-fire)
firearm which either has a barrel less than 30 centimetres in length or is less than 60 centimetres in length overall, other than an air weapon, a muzzle-loading gun or a firearm designed as signalling apparatus (e.g. pistols)
self-loading or pump-action rifled gun (other than .22 rim-fire)
self-loading or pump-action smooth-bore gun (other than .22 rim-fire or an air weapon) and either has a barrel less than 24 inches in length or is less than 40 inches in length overall
smooth-bore revolver gun other than one which is chambered for 9mm rim-fire cartridges or a muzzle-loading gun
rocket launcher, or any mortar, for projecting a stabilised missile, other than a launcher or mortar designed for line-throwing or pyrotechnic purposes or as signalling apparatus
air rifle, air gun or air pistol which uses, or is designed or adapted for use with, a self-contained gas cartridge system (e.g. BACS)
weapon of whatever description designed or adapted for the discharge of any noxious liquid, gas or other thing
bumpstock
disguised firearm

No licence is required for deactivated firearms, but as they are classed as "imitation firearms" the buyer must be eighteen or older.^{[source & source]}
Whilst a deactivation certificate (and Proof House stamp) gives the deactivated firearm the presumption of being incapable of discharging any shot, it is not required for a deactivated firearm to be sold (e.g. if the certificate has been lost).^[source]

A "realistic imitation firearm" means an imitation firearm which has an appearance that is so realistic as to make it indistinguishable from a real firearm from 1870 and newer; and is neither a de-activated firearm nor itself an antique.^[source]
The sale of realistic imitation firearms requires the buyer to have a defence, i.e., to make the imitation firearm available for one or more of the purposes specified:^{[source & source]}
the purposes of a museum or gallery
the purposes of theatrical performances and of rehearsals for such performances
the production of films
the production of television programmes
the organisation and holding of historical re-enactments
the purposes of functions that a person has in his capacity as a person in the service of Her Majesty
the organisation and holding of permitted activities (acting out of military or law enforcement scenarios for the purposes of recreation), for which public liability insurance is held in relation to liabilities to third parties [the airsoft defense]
the purposes of display at a permitted event (a commercial event at which firearms or realistic imitation firearms (or both) are offered for sale or displayed)
The sale of imitation firearms and realistic imitation firearms requires the buyer to be eighteen or older.^[source]

To be classed as an imitation firearm and not a realistic imitation firearm, the imitation firearm needs have the appearance of a design dating from before 1870, or to be made of transparent material, or the principle colour needs to be:^{[source & source]}
bright red
bright orange
bright yellow
bright green
bright pink
bright purple
bright blue
The sale of imitation firearms requires the buyer to be eighteen or older.^[source]
In summary: blank firearms, airsoft and other replica firearms that are "2 tone" or of old western/cowboy appearance only require the buyer to be eighteen or older.

Airsoft guns are not regarded as firearms as long they do not exceed 2.5 joules (518 fps at 0.2 g weight) or 1.3 joules (374 fps at 0.2 g weight) if they are capable of automatic fire.^[source]

The sale of air weapons and ammunition requires the buyer to be eighteen or older.^{[source & source]}
The power limit for air pistols is 6 ft. lb, the limit for air rifles is 12 ft. lb.^[source]
Those powered by carbon dioxide are still regarded as air weapons, this will include paintball markers.^[source]
Further reading: Home Office Guidance

The sale of knives, blades, swords and bayonets requires the buyer to be eighteen or older.^[source]
The above does not apply to a folding pocket-knife if the cutting edge of its blade does not exceed 7.62 cm (3 inches).^[source]
The sale of "offensive weapons"^[source] requires the buyer to have a defence, i.e. to make the offensive weapon available for one or more of the purposes specified:^[source]
the purposes of a museum or gallery
the purposes of theatrical performances and of rehearsals for such performances
the production of films
the production of television programmes
Offensive weapons that are antique (100 years old or older) are exempt from the above defence requirement.^[source]
Swords with a curved blade of 50 cm or longer (e.g. samurai swords) are also exempt if they are hand made using traditional methods.^{[source & source]}