Though some specialist carriers may also ship airguns the main allowed methods for domestic posting of sporting airguns within the UK are listed below:
Parcelforce 48 - But NOT Parcelforce 24, maximum insurance is £100. Can be shipped at a Post Office or Parcelforce Depot.
Royal Mail - All services allow the shipment of sporting airguns and airgun parts. First Class, Second Class or Special Delivery are all allowed. Note some Post Office staff may have a problem if you say you are shipping a gun, they may in error deem the gun as a prohibited weapon and not a sporting gun. You can argue your case with the manager but be prepared for a scared look on the face of some staff when you tell them you are posting a gun.
None of the above seem to allow pressure vessels so PCP guns may or may not be allowed and are sent at senders own risk. Very important CO2 CARTS MUST NOT be shipped via any of the above. If you ship a gun with CO2 carts inserted there is a good chance the gun will be sent to the Royal Mail Belfast Office, tested and destroyed.
References:
Royal Mail Rules - See weapons section on prohibited items. Low powered airguns are allowed.
Parcelforce Rules - See Arms and Ammunition section allowing low powered air weapons.