Higham, Lancashire born inside left Harry Hargreaves began his football career with Higham in 1913 and played for Great Harwood in 1914 before the interruption of the First World War, during which he served in the Army with The East Lancashire Regiment, reaching the rank of sergeant, and played Army football for the Regiment. He was wounded in action and detained as a prisoner of war for 18 months.
After the War he joined Central League club Nelson in July 1919 and when Nelson joined The Football League in 1921 Hargreaves played in their inaugural League match against Wigan Borough that August. After two goals in 13 appearances he was transferred to Second Division Wolverhampton Wanderers in November 1921, where he was a regular over the following two seasons, scoring 8 goals in 55 appearances. However when Wolves were relegated in 1923 he left Molineux, initially joining Pontypridd before being signed by First Division Tottenham Hotspur in December 1923.
In just over two years at Spurs he scored 7 goals in 34 appearances before joining Burnley in March 1926, helping them to narrowly avoid relegation at the end of the season. He stayed two more seasons at Turf Moor but was a fringe player, scoring 6 goals in 26 appearances before joining Rotherham United in May 1928. However he failed to make a first team appearance at Millmoor and joined non league Rossendale United in 1930, playing for Barnoldswick Town later the same year before joining Nelson Town in 1936 ahead of his retirement. After the Second World War, he became a director of the reformed Nelson F.C..