When I eventually got through to the BA Executive Club and complained, they first tried the usual "no planes could take off or land". When I said that a steady stream of planes were landing, I got, "Ah, we have to give priority to landing aircraft for safety reasons".
Far enough, said I, but you do realise Heathrow has two available runways, don't you? It's just that I couldn't see the take-off runway from the road.
The flustered ticket agent had said "only UK" flights were coming in, despite my seeing a 744 from another airline (looked like VS, but I was too far from the airport to be certain) landing.