I suspect that the arrival of a bunch of long-haul flights within 30 minutes of each other would test the processing capacity of any Border, anywhere.
I think that is one of the problems though. It's not as if they are surprised by the fact that a lot of long haul flights are suddenly turning up. This happens on a daily basis. Actually - maybe they are surprised by it and that's the reason why we have the queues!!
I can imagine the conversations
"Oh crikey more hoards of people coming though and we still haven't got enough staff"
"I know - that's the 5th time this week and it's only Friday."
"Weird - the same thing happened last week - what do you think's going on?"
I suspect that if BAA have resorted to handing out leaflets apologizing then the situation must be coming to a head.