Dolly
Knackered might be a better word than seriously tired. I'm surprised that a crew could be rostered a SSH-LXR in the same duty i must be getting old like BOAC. Fatigue will occur after a long summer perhaps not on just 1 flight. In theory CAP371 allows you to work hard during 7 days but if you do the 14 limits might counter it.
There's no doubt it was a long duty day and whilst the Commander may have said "no discretion" he's on slightly dodgy ground as BOAC states (although i offer every sympathy as he was probably trying to get the point over the duty was too long). It's one of those crew vv $$ for a crew change arguements, i'd take a bet BA would be changing crews,maybe