An Airgun is defined in the firearm act:
"Airgun' means any device manufactured to discharge a bullet or any other projectile -
a) of a calibre of less than 5.6 (.22 calibre); or
b) at a muzzle energy of less than 8 joules (6ft-lbs), by mean of compressed gas and not by mean of burning propellant"
Therefore, Airguns with a calibre of 5.6 mm (.22 calibre) and higher AND where the power limit exceeds 6ft/lbs are regarded as firearms and must licensed.
Airguns with a calibre of less than 5.6 mm (.22) do not have to be licensed. Therefor 4.5mm, 5mm and 5.5mm airguns do not need to be licensed.
Read the full Circular regarding the understanding when an airgun is considered to be a firearm - Implementation of the Firearms Control Act 2000 here.