Melissa's right that "Bringing Mary Home" is supernatural, but it's not a British song also found here in the US. Jane was asking about "Loss of supernatural story lines in American versions of British songs."

In fact, "Bringing Mary Home" is not actually a folk song, but a country song written in the last few decades that became popular on the bluegrass scene. I think it was first published in 1965 (that's according to the copyright database).

BTW, the same Urban Legend is the basis of Dickie Lee's "Laurie (Strange things happen)," a pop song also written in 1965.