<<Did LHR actually close in situations where there was a heavy storm on or near the airport or did it remain open regardless?>>
I've never known the airport to close except in some bad snow conditions so, yes, it remained open. Neither ATC nor the Airport Authority have the power to close the airport because of bad weather so far as I am aware.
<<Heathrow Director, IMHO, you ain’t seen nothing yet.>>
And I probable never will, Alf, having been retired for 2 years!. My comments are based on many years of experience - and extreme curiosity!
Happy cumulo-bumpulus!