Back in the 70s I think, two elderly gentlemen are sat in a retirment home/bedsit with copies of the Times and Telegraph (I think) reading the obituaries, having a game who died suddenly, peacefully, etc. and scoring on the results; I think it might have stared Richard Briers.
I'm a bit young to have seen this on TV, but I think it could be Home by David Storey. It starred Ralph Richardson and John Gielgud and was set in a psychiatric hospital. It was shown about 1971, so it could fit the bill.