How very strange. I travelled through LGW (London Gatwick) to the US back in 2003 taking a rifle an ammo I also flew Delta who were most helpful. I went to the check in desk a week before my flight and aksed the proceedures and am glad I did as the girls on the desk did not know so we got it sorted before hand. When I turned up I got special treatment as I as carrying a rifle. They took me to customs after checking in my suitcase with the rifle and it was checked against my firearms licence and my US form 6 and I was wished a successful trip which suprised me.
Heathrow is another story which is why I chose Gatwick
Now if you need to travel thorough the UK and have to change airports and you should know this before hand you can get a tempory Visitors Firearms permit and so take the firearms on the Bus or train or taxi which ever you shoose to use quite legally.
Just now with the hassle of no hand luggage I would not travel by air from the UK as I do not trust baggage handleers. My brand new alloy rifle case has some bad dents in it from that one trip. I carried my scope binos and camera in a back pack, the rifle is fitted with Apel roll off mounts which do return to zero
the ammo was in factory boxes which I pout into a steel 7.62 belt tin which I painted silver and wrote my name on it and packed in in the center of my suitcase with some brushes and jag and cleaning fuild in case the rifle got wet. The cleaning rod was in the rifle case under the foam.