Well that AA link is frankly cobblers
This is a copy paste from the Home Office Guide to Firearms Law.
the blue highlight is mine
What kind of firearm can be held on certificate?
1.3
Some firearms and shot guns may be held on a firearm or shot gun certificate
issued by the police. Low-powered air weapons are not licensed in England and
Wales unless they are of a type declared specially dangerous by the Firearms
(Dangerous Air Weapons) Rules 1969, but there are restrictions on their sale. An air
weapon is “specially dangerous” if it is capable of discharging a missile with kinetic
energy in excess, in the case of an air pistol, of 6 foot-pounds or, in the case of
other air weapons,12 foot-pounds. “Specially dangerous” air pistols (and certain
other air weapons) are prohibited weapons and may not be held on certificate.
See Chapters 10 and 11 (on firearm certificate procedure and shot gun certificate
procedure) for further details.