Widely sung by traditional singers? I didn't encounter the song until I saw it in a library book, when I was age 55 or so. I don't believe I have ever heard it in a concert.

This version, which uses five couplets instead of one to describe the killing, rather wallows in it, I think.

As for the ballad predating the Norman Conquest, I doubt it. In earlier centuries (I can't say which ones, exactly) infanticide was legal as long as any part of the fetus' body (a foot, for example) was still inside the mother's body.