Based on information from David Bazzard, Edward Copisarow and Dr. David Brown. The photographs of the Engine House and the Wheel were taken just before and after WW2 by Stanley Freese and are included here by permission of the Centre for Buckinghamshire Studies.
The wheel was used to pump water from a well above the lake (not from the lake) via 2 inch cast iron pipes to a covered holding tank above the house at Shardeloes. The tank was made from bricks which had been rendered and the flow was controlled by a very large copper ballcock situated in the tank.
It was in use until after WW2 when the house became empty. It is not known when it was built, but if it was first installed when the lake took its present shape it would have been in the mid 18th century. The mechanism could have been more recent.
The wheel was powered by water from the lake as an under-shot wheel and there was also a separate water feed which was over-shot.