An air rifle with a muzzle energy over 12 ft lbs or an air pistol over 6 ft lbs is called 'especially dangerous' and, as such, needs a section 1 firearms certificate (same as you would need for a .22 rimfire rifle, .223, .308 or such like)
Get caught with one without a certificate and you are in deep trouble and, to be fair, if you are going to the effort of obtaining a sect.1 certificate to do it legally, you may as well buy a proper rifle.
The difference between a sect. 1 and a shotgun certificate is that whereas the general presumption for a shotgun is that everyone is eligible to hold one and the police must prove reason why you should not, with a sect. 1 the general presumption is that nobody should be eligible and it is up to the applicant to prove why they should.
