My father was born in Todmorden, (West) Yorkshire in 1898. This is the version he taught me:

The Noble Duke of York
he had 10,000 men.
He marched them up to the top of the hill
and he marched them down again.
And when they were up they were up they were up,
and when they were down they were down,
and when they were half way up the hill they were neither up nor down.

My father would hold my arms as he sang, and raise them at the "up" lyrics, lower them on the "down" lyrics, put them half-way up for "half way up the hill."