I've not been able to find a psalm chant called 'Martyrs or Martyrdom' (but my resources are limited). I can only find the set chant for Ps 79 in 1900, being one by Samuel Sebastian Wesley (1766-1837) (Source - The New Cathedral Psalter Chants pub. 1909), which given the date of the Rowan Tree (1822 in the DT) is possible.... Wesley started writing music at an early age.

Otherwise, there is a hymn tune 'Martyrdom' written in 1800 by Hugh Wilson (1766-1824) which is another candidate. It has a psalmic feel to it and seems to have been used for many hymns, including Amazing Grace; O God of Bethel, by whose hand; Alas and did my Saviour bleed; and others. It's also known as 'Avon'.

LTS