June 6, 1925 – November 28, 1958: Age 33
Gareth Jones, a British actor, died during the live broadcast of a play on British television. Jones had a heart attack between two of his scenes; the rest of the cast improvised the play to its conclusion. The producer ordered the director to shoot the rest of the play "like a football match".
The play, Underground, was about survivors of a nuclear holocaust trapped in the London Underground. Ironically, his character was supposed to suffer a heart attack during the play: Jones actually had one.
(Pictured: London residents taking shelter in the London Underground during the blitz in WWII. Closest thing to relevant that I could find for this story.)
Sources: Wikipedia, IMDB, The British Telefantasy Timeline