Bob Bolton, I'm still curious about the tune that's been attributed to Sir Henry Bishop.

I must admit that I find the "it sounds Scottish so it must be" unconvincing. There were lots of Scottish immigrants in the US who had a huge influence on the music being created in the Southern Mountains.

Guest Q, according to Cyberhymnal, John Newton wrote the words for 288 hymns. He is given credit for 1 tune: Wonders.

Wilson's "Martyrdom," is indeed a very old Scottish Hymn tune, known by many other names. It's frequently called "Avon." It was added to the Sacred Harp (Denson ed.) in 1966 as "Sacred Throne," arranged by Hugh McGraw. It's also in Sacred Harp (Cooper ed), but I've forgotten the name it's under & the arrangement there is awful. It's also in the Primitive Baptist hymnal: The Good Old Songs by Cayce (1913)

I think it might be best known in the US for being used with "Alas and did my Savior Bleed?"

Here's a bit more I've been given from:
"The Presbyterian Hymnal Companion" by LindaJo H. McKim (Westminster/John Knox Press, 1993):

"MARTYRDOM was composed by Hugh Wilson towards the end of the eighteenth century. It was published in R.A. Smith's "Sacred Music in St. George's Church" (Edinburgh, 1825), where he designated it as an Old Scottish Melody harmonized by himself. The tune later appeared in "The Seraph, a Selection of Psalms and Hymns" (1827) and was attributed to Hugh Wilson. A copyright suit occurred. The outcome determined Wilson the owner of the tune.

"Recent studies have suggested MARTYRDOM was derived from an earlier Scottish folk melody. The tune has also been called FENWICK, INVERNESS, AVON, ALL SAINTS, BOSTAL, and DRUMCLOG.
      
"Hugh Wilson (1766-1824) was born in Fenwick, Scotland, studied mathematics, and worked as a calculator and draftsman throughout his life. He led the psalm singing in the Secession Church."