Allison was born in Edinburgh.[1] He joined Hibernian from Junior club West Calder United in January 1958.[5] He scored on his Scottish League debut that October, in a 2–1 win at home to Clyde, and produced three more goals in his and Hibernian's next four matches, but made no more appearances for them.[6] At the end of the season, he moved down a division and signed for Dumbarton,[7] scoring four goals in fourteen league games[8] before moving on again in January 1960, this time to fellow Second Division club Cowdenbeath.[9]
He moved to England in 1963 to sign for Fourth Division club Darlington, for whom he scored a goal every two games.[2] In February 1966, Allison joined Lincoln City in part-exchange for Barry Hutchinson, in a deal estimated by the Guardian at about £5,000,[10] as Darlington reinforced an already strong squad to ensure their first promotion for more than 40 years.[11] Allison scored seven goals in his twelve appearances in what remained of the 1965–66 season, but was less productive the following year,[1] and left Lincoln to play in the American Soccer League for the Rochester Lancers in 1967. He remained with the Lancers until 1970, when he joined the Syracuse Scorpions as part of the deal in which top scorer Jim Lefkos moved to Rochester.[4]
