Denny started diving in 2005. His first achievements at international level came with the 2011 Junior European Championships where he classified 4th from the 1 m springboard and 6th from the 10 m platform. During the period 2011-2014 he competed at the British Championships, where he collected several medals.
He represented England at the 2014 Commonwealth Games, winning a silver medal alongside his partner Tom Daley in the 10 m platform synchro, and classifying 6th in the individual event. Also during the same year, he took part in the 2014 European Aquatics Championships, where he missed on a bronze medal in the 10 m synchro event alongside Tom Daley and achieved a 12th place in the individual final.