That song struck me as wrong, too. Maybe, just maybe (though I'd still doubt it) if the troops were American. But not if they were English.
The film was very good -- I saw it three days ago. Not "great", but above average and a good way to spend a couple hours.
I don't particularly care for "modern" (20th century) war films. The exceptions (in my book) are "Paths of Glory", "The Train", "Dirty Dozen", "Three Kings", and "Dunkirk". And the only Vietnam film I could bring myself to watch was "Good Morning, Vietnam".
I found, in quality, "1917" to be not quite as good as "Dunkirk", but not as bad as "War Horse" (aka "Black Beauty In the Trenches").