Only running from the simple question put to the Author Alan Clark i.e.
Question "Where did it come from?

Answer from Alan Clark "Well I invented it"

I've got no difficulty in understanding that, we know that the man was a dissembling liar, and I most certainly do not give much credence to a "so-called-historian" who simply makes stuff up. Particularly when many others take the trouble and do the work to get things right.

If the book was considered to be the inspiration for the play then it logically turns out that "Oh What A Lovely War" can only be classified as being shit based on shit.