What you are doing is Hidden City Ticketing where A to B is more expensive then A to B to C so you get off in city B and go home.

Not sure how the UK based airlines (BA) feels about this practice but in the US the airlines are not to pleased when people do it. There is a company here in the US called Skiplagged and they show flyers how to utilize HCT. UA's reaction to this was to sue them.

HCT is against the T & C of the US based airlines and they can, theoretically, if you did it enough, suspend your FF account and take your miles. That being said, if you do it occasionally you probably will have no problem.

Do not tell the airport staff that you are not taking the last leg. They can, again theoretically, try to charge you for A to B, since that's what you flew.