I can tell you that there are a number of versions, with different heroes' names, with basically the same story line. Some have other tunes, or at least major variations on the tune most people know.
I do not claim to be an historical ethnomusicologist (a person who studies different cultures' music from a historical perspective) but in fifty years of singing and playing this song, and hearing it played and sung, I've never heard an attribution to a particular author.
I BELIEVE (and one of the Mudcat experts can and surely will correct me if I'm wrong) that Henry Martin is one of the songs we refer to as Child Ballads. This expression is from Professor Frances James Child, an American professor who is one of the sainted names in the study of folk music, and especially the English and Scottish popular ballads. I doubt that he would have included it (them) in his collection if the author was known.
I hope this is helpful.