"He does not leave any family but a host of friends who were his chosen family.
"His death is a great loss to them and the profession."
Actors and comedians took to Twitter to pay tribute to their friend and colleague.
"Very saddened to hear about Sam Kelly's death," Stephen Fry tweeted. "He played a splendid Hitler in a comedy drama called Stalagluft I made with Nick Lyndhurst..."
Former Doctor Who Colin Baker tweeted: "Cannot believe that lovely Sam Kelly has died. We were at drama school together - lovely, funny, talented chap. So sad."
And Sherlock actor Mark Gatiss said "desperately sad news that the wonderful Sam Kelly has left us. Such a funny, talented man and one of the good guys. RIP Bunny Warren".