I do not know when I first heard and learned "I know an old lady who swallowed a fly" but it must have been in my early teens, perhaps when I was a sea scout, and the singer was probably Burl Ives. I sing it very often and it goes down well with German audiences. Because they are generally first-time listeners, the punch line "She's dead, of course!"
always brings laughter.
Since writing the above sometime in 1999, I've now (July, 2019) found that the song was the work of Alan Mills
who, together with ose Bonnet (lyrics) copyrighted it in 1952.