I sat in Club a while ago whilst taxying out on an ATL flight listening to a cc dscribe how they had diverted to Stansted yesterday on a back to back, got transport back to LGW by late pm but still checked in for 9 am check in. By my calculation they were way out of duty hours, but their topic was the extra money involved made it all worth while. With the BA system I doubt the Captain was aware of his cc hours.
Now you're just making stuff up.
Let us know the FTL details but I cant see any way that a 2 sector ex USA day would make a following days trip illegal. The max duty time is simply not enough.