Let me please name drop. I once got stuck in the lift with the late Sir Robin Day (God rest his soul) in Terminal 1. I don't think it showed his best side.
In Terminal 5 it is a big problem. So much so that in the most prone lifts there is a little sign begging people not to call 999 if the lift breaks down, unless it's a medical emergency. Apparently the Met Police has given BAA grief on the issue.