In regard of the aforementioned US transfers, APD is not payable by inbound international passengers who are booked to continue their journey (to an international destination) within 24 hours of their scheduled time of arrival in the UK.
For APD purposes UK originated connected flights are treated as one journey and APD is charged according to a passenger’s final destination irrespective of the number of flights that they take to reach this, provided the flights are connected. In the case of all connected flights, it is the first uplifting carrier who is liable for APD.
http://customs.hmrc.g...propertyType=document
If your question is in relation to an unscheduled stop then it would be a very passenger unfriendly airline who would charge you any extra of their liability to pay higher APD in addition to the inconvenience of interrupting your journey.