In May/June this year I did the Phoenix - London - Jo'burg route. As mentioned you will need to inform BA of your intention to fly with firearms sometime before your flight, I'm think it's 3 days or so. Pretty easy really. At Phoenix Sky Harbor there was a bit more of a process to get the rifles on board, but nothing to get in a twist about, just make sure you show up plenty early.
Arrived Terminal 5 in LHR and found I had to essentially repeat the process of going through security. Whether or not I was traveling with firearms is irrelevant, I would have had to do this anyway. But it is one more added hassle in comparison to flying directly to Jo'burg from Atlanta on Delta. Not too big of a deal, though when going back home I was selected to have my carryon bags dumped by security. I have no idea why, they just did.
Life in Terminal 5 is about as good as life in an airport can get I guess. Plenty of restaurants and plenty of shopping. But how 5 hours +/- was as much as I can handle. But that's also less time than what you'd need to leave the airport, get into London proper, do some tourist things and then get back to the airport and go through security. If you don't have a bit more time than that, you'd better stay at the airport.
While in London, not word about my firearms. Everything was handled without any fuss other than what I went through in Phoenix. I kept my paperwork through my trip and provided the copies given me when I checked in to go home. A bit of the same hassle in Jo'burg. The lady I checked in with was less familar with the BA way of doing things slowed me up a bit. But she didn't cause me any problems, it just was slower than it needed to be.
Would I do it again? If I was saving a bunch of money on air fares, yes. But if it was roughly even, no. Nothing against BA's process of transporting firearms or any other issues, I just wouldn't want the layover in London again if I could avoid it.
