"La Madelon" - Lyrics Louis Bosquet (1914), Music by Camille Robert.
English lyrics- Alfred Bryan.

Lyr. Add: "Madelon" (English version)
"I'll Be True to the Whole Regiment"

There is a tavern way down in Brittany
Where weary soldiers take their liberty
The keeper's daughter whose name is Madelon
Pours out the wine while they laugh and "carry on"
And while the wine goes to their senses
Her sparkling glance goes to their hearts
Their admiration is so intense
Each one his tale of love imparts
She coquettes with them all but favors none at all
And here's the way they banter ev'ry time they call-

Chorus A
O Madelon you are the only one
O Madelon for you we'll carry on
It's so long since we have seen a Miss
Won't you give us just a kiss
But Madelon she takes it all in fun
She laughs and says "You'll see it can't be done
I would like to but how can I consent
When I'm true to the whole regiment."

Chorus B
O Madelon you are the only one
O Madelon now that the foe has gone
Let the wedding bells ring sweet and gay
Let this be our wedding day
O Madelon sweet maid of Normandy
Like Joan of Arc you'll always be to me-
All through life for you I'll carry on
Madelon, Madelon, Madelon!

He was a fair-haired boy from Brittany
She was a blue-eyed maid from Normandy
He said Goodbye to this pretty Madelon
And went his way with the boys who carry on
And when his noble work was ended
He said Farewell to his command
Back to his Madelon he wended
To claim her little heart and hand
With love light in his glance
This gallant son of France
He murmurs as she listens with her heart entranced.

http://www.pdmusic.org/1900s/18madelon.txt

Quite different from the original song.
So far I have been unable to find any of the verses of the British troops.