I called BA who said, as Swanhunter and others suggested, that I needed to arrive in time for the originally scheduled flight, because a flight time might be moved up. So, I followed the advice.

However, when I went into the lounge, the person at the desk said I could have come later because the reason for the delay was that last night's plane had arrived late and by law (FAA regulation?), the crew was required to have 8 hours of sleep. So there was no way it could leave before 9:30.