A poem about a mouth organ player at the battle of Passchendaele, has just featured on the BBC website:

http://www.bbc.co.uk/news/uk-scotland-40739915

Here's the poem, from a regimental history site:

http://1914-1918.invisionzone.com/forums/index.php?/topic/199719-9th-battalion-black-watch-july-1917/

THE MOUTH-ORGAN

When drum and fife are silent,
When the pipes are packed away,
And the soldiers go
Too near the foe
For the bugle's noisy bray ;
When our haversacks are heavy,
And our packs like Christian's load.
Then Jimmy Morgan*
Plays his old mouth-organ.
To cheer us on our road.
"It's a long, long way to Tipperary"
When by the shrunken river
Reclined the great god Pan,
And to his needs,
Cut down the reeds --
And music first began ;
Then all mankind did marvel
At a melody so sweet ;
But when Jimmy Morgan
Plays his old mouth-organ,
Even Pan takes second seat !
When Orpheus, of old time,
Did strike his magic lute,
He lorded it.
As he thought fit.
O'er boulder, bird, and brute ;
And great trees were uprooted.
And rootmarched, so to say.
But when Jimmy Morgan
Plays his old mouth-organ,
You should see us march away

Though for obvious reasons of rhyme I have here ventured to appropriate the classic name "Jimmy Morgan," nevertheless the best mouthorganist in D Company, if not in the battalion, is 2203 Private William Brough. He informs me that his present instrument is something the worse for wear.

It would be great to have a tune for that.

I know one other piece featuring mouth organs in WW1, and it's from the Turkish side, a song with four alternate titles, "The mouth organ was played", "Yemen Song", "There is no cloud in the sky" or "This is Mus", about the soldiers from the mostly Kurdish village of Mus who went away to fight in Yemen on the Mesopotamian front and never returned. This version begins by describing how the soldiers are playing mouth organs on their way to war as if for a wedding.

version with lyrics in the comments

There are many versions of this on YouTube, it's one of the most popular of all Turkish folksongs. Here's a collaborative performance, packing in more different styles than I would have imagined possible, from folk ballad to Turkish classical to heavy metal:

https://www.youtube.com/watch?v=t4DBc0z7ki4