G'day,
The Australian Hymn Book has quite a few hymns, traditional and set to trad tunes.

e.g. From thee all skill and science flow (Dives & Lazarus/Star of the County Down) words by Charles Kingsley 1819-75

Kneels at the feet of his friends by Tom Colvin (c.1965) set to a Ghana folk melody.

I bind unto myself today/Christ be with me - attributed to St Patrick. etc. etc.

Cheers,
Alan