I heard this haunting melody as background music in a movie, suspected it was an old English hymn, and Patty and I found it on the Internet: Down in Yon Forest, here performed by the folk group, Kerfuffle.
This hymn, usually sung at Christmas-time, goes back at least to the 14th century ande may be older than that. It likens Our Lord Jesus Christ to a brave knight who sheds his blood for those who love him.