Hi craig as recently i have just done this, this is what i found out:
Most big airlines will take firearms if air rifles u will need to empty the air cylinder and check it as normal baggage, u will just have to take it to over size baggage, they will charge u for 1 gun case the same as and extra peice of luggage so forth,
U will have to ring the airline and let them know around 2-3 weeks before your flight.
There should be no Inspection in the uk if there is they use a machine bit like and xray,
This was with BA
Now on the other side customs can do what they want believe me!! if there