I once visited a Country House named on the outskirts of York--
   where it was said the rhyme fist originated, the story told of The Duke of York commitioning 10000 men to build him a large and very deep lake in the grounds, they dug down and the soil was then taken to a site also in the grounds to build a huge hill, hense when they were up they were up and when they were down they were down.
Ive also heard the verses using the drums and flutes but never heard the story behind them.