I've got in front of me a book I bought in a jumble sale or somewhere years ago, called "The Minstrelsy of Peace", edited by J.Bruce Glasier, and published by the National Labour Press Limited (Manchester and London): "A Collection of notable Verse in the English tongue, relating to Peace and War, ranging from the fifteenth century to the present day."

It doesn't have a publication date, and it's not clear whether it was published during what it refers to as "The European War" or immediately after.

As the summary indicates, it's mostly older stuff gathered together, including some traditional songs such as "The Rambling Soldier" and "The Pressed Man's Lamentation".

In the section on "The European War" it's got various poems by writers including Siegfried Sassoon and Wilfred Wilson Gibson.

A couple of the latter writer's poems which are included, which have been anthologised fairly widely, would I think make a great song, and feel like they might well have been written as such, though I've never heard them sung. (They're very reminiscent of AE Housman's "Shropshire Lad"):

IN THE AMBULANCE
"Two rows of cabbages
Two of curly greens,
Two rows of early peas,
Two of kidney beans."

That's what he is muttering,
Making such a song,
Keeping other chaps awake
The whole night long.

Both his legs were shot away,
And his head is light;
So he keeps muttering
All the blessed night -

"Two rows of cabbages
Two of curly greens,
Two rows of early peas,
Two of kidney beans."

and the other one is

RAINING
The night I left, my father said:
"You'll go and do a stupid thing.
You've no more sense within your head
Than silly Billy Withering.

"Not sense to come in when it rains -
Not sense enough for that you've got.
You'll get a bullet through your brains,
Before you know, as like as not."

And now I'm lying in this trench,
And shells and bullets through the night
Are raining in a steady drench,
I'm thinking the old man was right.