Did BA advise/warn staff that monitoring was a possibility? Surely if it was their intention then staff should have been told. Does the same apply to desk-tops in offices? One hears stories throughout the office world of how much surfing is done by staff during the working day. It could be during lunch/break times, but it is still on company equipment.
It's not quite so simple. Thus it needs to be clarified. Think what the reaction was to the idea of cockpit cameras. This isn't quite the same, but people like to protect privacy, but as others have said why not separate private and company toys.