Going through LHR T3 on Wednesday 4th, I allowed the maximum amount of time and ... sailed through. The fast through time I can recall.
We go to the upper level around 16:30 and were though to shops in 10 mins flat, so something had obviously gone terribly wrong!
That is the problem - pot luck. You never know if it is going to be good or bad and it might be good, simply because you arrive at a natural low spot and if you arrived ten mins later it would be tea breaks and five coach loads at once.