Sunderland born, Harry Oliver played both full back and centre half during his career which spanned both sides of the Second World War. He played for Doxford Juniors and Hylton Colliery Juniors as well as Ditchburn’s, and in Sunderland’s A team, and represented England as a schoolboy before joining Houghton Colliery Welfare in 1936. He joined Sheffield United as an amateur in May 1937 without playing for their first team, and then joined Hartlepools United in October 1937, turning professional in March 1938. It was while with Hartlepools that he made his Football League debut against Doncaster Rovers in March 1938, and after 9 games only he was bought by First Division Brentford for £1500 in May 1938.
He didn’t get to play in the Brentford first team before the outbreak of the Second World War, during which he guested in wartime football for Leeds United and York City, making his official Brentford debut in an FA Cup tie against eventual finalists Charlton Athletic in January 1946, playing in both legs as they were beaten 9-4 on aggregate.He then played only 18 League games for Brentford before Watford bought him for £2000 in May 1948, where he enjoyed regular football during his 4 seasons with The Hornets, scoring 4 times in 128 appearances and endearing himself to the Vicarage Road crowd with his forthright defending. He joined Canterbury City at the end of the 1951–52 season, and remained there until his retirement in 1956.