There are lengthy and heated threads on this.

The competing views are: (a) if you drop the last sector of an ex-EU BA is entitled to charge you for the difference between your ex-EU ticket, and an ex-LHR ticket plus a one way from EU to LHR. And possibly delete your Avios, expel you summarily from the BAEC, and pretty much anything else it can think of. (b) BA's remedy under its CoC is to refuse to carry you further on the ticket and that's the totality of its remedy, which amounts to nothing if you drop the last sector.

AFAIK whatever the position may or may not be with other airlines, BA has not taken a stand on this - yet.



The wording is slightly odd (read: inept), since the extra charges threat arises if you don't travel to your final destination. If you travel with HBO, the warning might lead one to think that there is no risk of an extra charge, which I doubt is BA's intent. Likewise if you have an airport change in London and want to (and do) take the final sector without hold luggage.