Well, my two previous responses on this have evidently disappeared into
oblivion, so here goes again...

The one where the actor died during a live broadcast was an Armchair
Theatre production called "Underground" (broadcast November 28, 1958)
about nuclear war survivors. The actors were supposedly digging their
way out, and were "rotated out" to have more make-up progressively
applied so that they appeared dirtier as time went on. One of the
actors, Gareth Jones, complained of feeling unwell while off-set and
collapsed from a fatal heart attack. The script was hurriedly re-written
to cover his absence. Of note is the high quality of the other cast
members including Peter Bowles, Andrew Cruickshank and Warren Mitchell.