I always thought it was Highland Division as in 51st Highland Division. There were plenty of Poor Scouser Tommys who fought and died in WWII in the Highland Regiments of the 51st.
Of course it comes down to aural tradition and nobody will know (kind of chinese whispers). I heard "higher division" as a boy.
After all, there was a famous battle at spoin KOP in the mountains of south Africa. After which the kop was named.
"Many football grounds in the English Premier League and Football League, and several in the American, German, French, Hungarian, Japanese, Northern Irish and Scottish leagues, have one terrace or stand in their stadia named "Spion Kop" or "Kop" because of the steep nature of the terracing"http://en.wikipedia.org/wiki/Battle_of_Spion_Kop
The regiments that fought included:
"2nd Kings Royal Lancaster Regiment
2nd Lancashire Fusiliers
1st South Lancashire Regiment
1st York and Lancashire Regiment"
In those days Merseyside was part of Lancashire.