Hodgkinson made his league début in Division One in a 2–1 away victory against Newcastle United on 28 August 1954 but, despite showing his undoubted potential, the presence of number one goalkeeper Ted Burgin until 1957 and National Service limited his opportunities for the first team. The arrival of Joe Mercer as manager established Hodgkinson's place as first-choice goalkeeper in the side behind the defensive line of Cec Coldwell, Graham Shaw, Brian Richardson, Joe Shaw and Gerry Summers. In 1966–67, he won the Sheffield United Supporters player of the year award. His brilliance and reliability made sure of his place until the signing of John Hope in 1971. His final appearance was, like his first, in a friendly, on 23 January 1971 against Chesterfield.