A quick update for Saturday.
There are just 3 cancellations I can see (BRU, IAD, FCO) and they don't seem to have anything to do with the events yesterday. No Germany, AMS, ZRH cancellations. I will list them in an hour or so in the main FAQ thread. As things stand BA has 332 flights departing today, out of LHR's total of 657 - these are both high figures for a Saturday but represents the slide to the school holiday period in England and Wales. Timekeeping isn't very good at the moment, BA is 57% on time departures, 73% on time arrival. However that's based on a small number of flights so far, e.g. only 90 of the 657 departures. The ATC report is fairly unexciting, but there may be some cumulonimbus issues in the evening, but the number of flights on a Saturday evening may balance that factor out.
So it's probably just baggage reclaim which will annoy passengers today, and maybe some morning queues, but that's just sheer weight of passengers and bags on a holiday weekend.