I think this is a BA procedure only. Unless all other carriers are just breaking the law but I doubt.
I anyway believe it is important to check boarding passes just before boarding the A/C.
This specific part is the one that is open to different interpretations: BA has adopted the strictest view.
To check b/passes just before the Loading bridge or immediately before stepping on the aircraft it is a choice of each carrier, this is open to all interpretations but BA is free to recheck again and again if needed.
This does not mean that checking only in the lounge just before boarding is not as secure as the BA procedure. It is only that the BA interpretation of this CAA rule is that the b/passes must be checked again on the A/C door.
Please advise if this is wrong.