My sympathies to the OP - it doesn't sound like a great experience and it's easy for us who use LHR weekly to know what the conformance requirements are. I think that these kind of restrictions could be more clearly explained, on the app, in pre-departure emails etc. I do think that BA is probably pretty well covered legally on this but it's disappointing that they don't seem to have tried to help.

I've only twice had notifications to arrive late to the airport due to a late departure which BA knew they couldn't recover from - both times at outstations (ICN and HKG). These notifications tend to come by SMS and / or email.

I do remember a couple of years ago an initial 6-hour delay to an HKG flight from LHR one day when there was no notification to arrive late to the airport (the A380 had been hit by lightning). In the end we departed 3 hours late on a 777, so delays can be brought back in.