on a BBC radio show called the Goon Show, which ran from 1951 to 1960, the joke is credited to Spike Milligan, as an aside he is often remembered for his headstone, He had once joked that a suitable headstone inscription would be "I told you I was ill" and that is indeed what is on his own headstone, the words are, in a reference to his Irish ancestry, (and because the local Diocesan authorities thought it too lighthearted an inscription to be engraved in English), in Gaelic, the full version reads:
Love, Light, Peace
I told you I was ill
but on to the world funniest joke he told on radio, here it is,
Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy goes to a telephone and calls the emergency services. He gasps, "My friend is dead! What can I do?" The operator says, "Calm down. I can help. First, let's make sure he's dead." There is a silence; then in the distance a gun shot is heard. Back on the phone, the guy says, "OK, now what?"