That's not an uncommon problem with all reservations engines. They want to sell the same fare to everyone in the party.

For future reference, you might want to check fares on AA.com (or other U.S. reservation engines) first as it often sells and quotes lower fares with less tax than BA.com and other European reservation engines.

Last week, I bought 2 LHR-LIS tickets on BA that, for the exact same flights, costed some GBP 30-40 each less at AA.com than BA.com.