Looking closely...

The webby says:

Guns intended for sporting purposes - including Section 1 (e.g. hunting rifles) and Section 2 (e.g. shotguns) firearms, low-powered air weapons and their component parts - may be sent in compliance with UK law and subject to domestic controls on the possession of firearms. Antiques, deactivated and imitation firearms are also permitted. When sending deactivated firearms include proof of deactivation.

Items that appear to be prohibited weapons may be subject to additional checks and delays. Please see www.royalmail.com/prohibitedgoods

Use 1st Class as the minimum service. The sender’s name and address must be clearly visible on the outer packaging.

If you click on the prohibited goods link - Airguns are listed but says (in full):

Guns for sporting use (Section 1 and Section 2 firearms, low-powered air weapons and their component parts) Packaging guidelines: May be sent in compliance with UK law and subject to any applicable controls on the possession of firearms. Only low-powered air weapons are accepted by Parcelforce Worldwide and must be sent using express48 via the Post Office. Sender’s name and address must be visible on the parcel.

So RM accept Section 1/2 and AG's, whereas PF will only accept AG's - or am I reading it incorrectly??