I set Henry Lawson's WWI poem, The Route March, to music: it's recorded on my album The King's Well.

Of course, Robert Burns set many of his verses to traditional tunes. There are umpteen recordings of these -- take your pick.

Also poems by Sir Walter Scott. E.g., Jock O'Hazeldean is half trad., and half his -- there are recordings by Alex Campbell and Priscilla Herdman.
Then there's Violet Jacob's wonderful poem The Wild Geese Flee, which Jim Reid put to music: he sings it on one of his albums, and so does Cilla Fisher.

Another Scots poet, Lady John Scott (Alicia Spottiswoode) set her own poems to music; but my favourite of these is one that Archie Fisher sings (possibly his own tune?): Ettrick. On his album with Garnet Rogers, Off the Map.

And then there's Lady Nairne: Jean Redpath (who has also recorded
many Burns poems/songs) has an entire album of these poems.

For Irish poems: there's The Gartan Mother's Lullaby -- which many recording artists seem to think has traditional words. T'ain't so! The lyrics are still under copyright: the poet was Joseph Campbell, and his son Simon (living in Ireland) holds the copyright.

Padraic Colum's poetry has also been set to music.

It's too late at night here (in Jerusalem) to think of any others, but I'm sure I'll think of more in the morning.

G'night!

Jill