Garry RF and PHeymont - Thank you very much for the information.
In this case, APD is not incurred -
Flying NYC-LON-Continental Europe: No problem; as long as your time in UK is less than 24 hours, you are a transit passenger and don't pay APD.
In this case, there is an APD, even if the transit is less than 24 hours ? -
Flying Continential Europe-LON-NYC: Not so good; you pay the APD on the trans-Atlantic leg, and that's high.
Concerning the third item, this explains why Worker Bee had a problem with his particular booking, because, to connect through London, AA would book him on their partner BA, or a BA operated flight, for the jump over the Atlantic, yes ? -
The other issue with this is not APD at all; flying to the Continent through Madrid or Barcelona tends to be cheaper because it usually doesn't involve BA, which has the highest "fuel surcharges" of any of the Oneworld partners.