Working with the TCM list and listening to clips, I was able to match most of the tunes with where they occur. I could still use help with the remaining bits. Changes shown in bold.

0:05 Rhyfelgyrch Gwyr Harlech (Men of Harlech): Title music
3.50 Cwm Rhondda (Rhondda Valley): Men walking home from mines
12:00 Calon Lan: Wedding: walking up the aisle
13:40 Llwyn on (The Ash Grove): Wedding: procession out of the church
14.10 Hob y derry dando: wedding: bringing out the cake
15.15 Peter O'Pea (Here's a man won't get drunk): wedding celebration
16:00 Mochyn du (The Black Pig): Wedding celebration
34.50 Mentra gwen (The stars in heaven are bright): serenading mother on recovery
36.05 Myfanwy: same scene, mother at door
48:30 God Save the Queen: in church, after receipt of royal invitation
53.10 Penparc: hymn in church
1.05:38 Cwm Rhondda: Angharad's wedding procession (same as an earlier song)
1.20:17 ??: Death of Ivor
1.27:10 Bryn Calfaria: Men walking to mine
1.41:40 Llef (aka "Deus salutis"): hymn
1.52:10 ??: descent into mine after the explosion
1.56:xx ??: ascent from the mine with the body
1.56:45 Myfanwy: ending
1.57.52 ??: film credits

Notes:
Calon Lan: Gwyrosydd (lyricist) = Daniel James (1847-1920).
Llef: by Griffith Hugh Jones (Gutyn Arfon), Gemau Mawl, 1890; written in memory of his brother Dewi Arfon (David Hugh Jones).
I Saw a Tiny Streamlet: Owain Alaw [Pencerdd] = John Owen (1821-1883).

No clue about "The Sixpence" or "I Saw a Tiny Streamlet" (though I suspect this is the music for the end credits).