You can send air weapons through normal post too - it's a restricted item, not a prohibited one - it's even on Royal Mail's website

https://personal.help.royalmail.com/...detail/a_id/94

The only things prohibited are Section 5 and illegal weapons.

I'm not sure where the PF48 thing came about?

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.
I've recently received 2 rifles through PF and both arrived perfectly safely, mostly as a result of the good packing by the sender!