BA's policy in the event of any disruption at LHR is to cancel , particularly short haul ,flights for its operational convenience. As result they have become the worst choice airline to book with on such a day. The sheer numbers of their passengers make it impossible for them to do much for the passengers on the cancelled flights other than offer compensation or refer them back to their pcs to try to make new bookings. The predominance of e-tickets and lack of manual systems or agreements to pass passengers on to other airlines means that they can not just send them over to LH, AF etc even when these have empty seats. The days of manual systems were very customer friendly in comparaison.
The root of their problem is their failure to secure Union agreement for pilots (other than on the first transit of the day) and cabin crew to treat LHR as just another transit airport so the crews have (different) minimum base turnaround times so that they can come off the aircraft, go and have a coffee and a bun, ring Mum or whatever. Hence the aircraft, pilots and cabin crew are all rostered separately through LHR and do not stay together for their complete shift as do most and especially Easyjet and Ryan whose shorthaul systemwide punctuality knocks the socks off BA. Hence once inbound delays start happening the whole programme comes unstuck for the rest of the day and the cancellations roll in. Domestics seem to take the worst hit, on the basis that there are alternatives, highly inconvenient and impractical though they may be. The whole situation is a disaster and unique to BA at LHR but solving it appears to be a low priority. The issue was raised recently in the Scottish Parliament but it's doubtful if anyone was listening. Until a few years ago the policy was to do everything possible to fly the plan, even if delayed, and end the day with everyone possible where they had hoped to be but operational convenience now over rides customer service,- now an almost derided term.