According to this Wikipedia article, Derby School is a very old institution which has "had an almost continuous history of education of over eight centuries." In 1863, the school moved to St. Helen's House in King Street, Derby, which had been owned by Edward Strutt, 1st Baron Belper, and over the next 25 years, "was expanded from a local grammar school into a nationally known public school ... The school was greatly expanded with 'B'-block being added in 1901 ... During World War II, the school was evacuated to Overton Hall, Ashover, a village near Matlock," although it returned to St. Helen's House after the end of the war. The image below is a recent picture of "B" Block, St Helen's House, and it is clear that it is was infront of this building that the cadets sat for the portrait.
"B" Block, St. Helen's House, Derby in 2007, from Wikipedia
Are there any readers out there who might be able to identify any of the men in this picture. Please email me if you would like a high resolution version of the image.