This is one of the twin pumping stations powered by coal and steam at Little Eaton Water Works and commissioned by Derby Corporation Water Works.
(extract from leaflet about the contruction of the new works at Little Eaton 1959):
These Works were originally laid down by the Derby Waterworks Company as a pumping station only, in 1850, and included steam driven pumps arranged to deliver water which gravitated into a large collecting tank from infiltration galleries laid alongside the River Derwent, to the Low Level Works on the hillside to the east of the Pumping Station. Additional pumping plant was added in 1875 to deliver water to the newly constructed High Level Works, of similar general design to the Lower Works, and from that date, with the exception of the provision of some temporary pumps about the turn of the century, which were later removed, no further additions were made to the plant until 1935, when two electrically-driven centrifugal pumps were installed to take over the duties of the steam plant.
Photo supplied by Alan Gifford and is from The English Heritage collection web site.