Possibly W.H. Day.
Derby Daily Telegraph 21 February 1910 mentions a W.H. Day of Derby described as a long-standing member of BH and one of its finest long-distance runners.
William Henry Day, service number 200806 of the Sherwood Foresters (Nottingham and Derby Regiment) 16th Battalion, was killed in Flanders 23 November 1917. He died from his wounds.
Not conclusive, needs more research.