SOP
A 'Provisional Loadsheet' system is used at BA to assist on time departures.
So-called 'Final Figures' are then passed to the crew via ACARS which are either 'No Change' or 'Last Minute Changes' (LMC) dependent of the magnitude by which certain of the provisional parameters change from the point of push back.
The latter requires reprogramming of the FMC and cross-checking by the handling pilot. It also requires the aircraft to be brought to a stop due to the possibility of distractions occurring. Some macho pilots ignore this and continue taxying.
On this service approx 1,000 kgs of freight no-showed, but due to another BA flight to LHR being oversold there were some additions in the passenger load. However, the net change in ZFW and index was small , thus an 'LMC' was not triggered.
This removes any possibility that the crew would have been distracted by BA's SOP's per se.
On the the other hand we know BA leave pilots roundly unpunished for sending a lewd sexual texts whilst uniformed, on the flight deck and operating flights in direct contravention of the law and their employment contract - if you don't believe this sort of thing goes on just 'Google' the following 4 words 'Sun newspaper pilot text'.
Now, I'm not saying this was the case here, but maybe just maybe the crew dropped their guard and became distracted by non essential tasks.
Either scenario is negligent and sackable.