Did LHR actually close in situations where there was a heavy storm on or near the airport or did it remain open regardless?
I think the main problem (apart from the fact that as
HD says, ATC can't close it except for u/s runways) is that ATC in the UK are blissfully unaware of any weather as they don't have it on their screens.
This is a major drawback as most of the airtime on a CB day is taken up with requests for weather avoidance, especially when a storm drifts through one of the holding patterns. It is annoying to get a heading which takes you right through the middle of an ugly red patch - this is the ONE area where I prefer flying in the USA (not that it's the fault of the UK controllers).
Also, not all airborne weather radars are created equal (or even operated in a consistent manner) so everyone sees something slightly different, which must be even more confusing to the audience on the ground...