I meant to say that there may be no availability in 'H' class a few days before the flight as the flight may be full and BA won't want to sell less expensive ticket. If 'H' is available you'll be rebooked into 'H' with no extra charge but if 'H' is not available you'll need to upgrade to 'B' or 'Y'.
I also thought that when you change you need to observe advance ticketing conditions for many fares...