kmcottrell…sorry was not clear….the discount applies only to BA flights booked on ba.com. it specifically excludes hotels cars and coeshares parking and everything else on the site for the reasons given by disgustedofSwieqi. Once you take another element you tranfer the bookeing to BA holidays and you get the benefit of their deals but not the shareholder discount.
As many have noted it is often cheaper to by a package says LHR JFK LHR with 3 nights in a JFK hotel than it is to buy the airfare alone. I have myself taken advantage of this and have only once used the hotel element. The savings can be considerable and far in excess of the 10%.
Another option is to start in Europe where fares on BA can be half that of originating in the UK and the shareholder discount still applies. You can then book the hotel separately