He scored 23 League goals in 74 appearances, and 7 FA Cup goals in 12 appearances. Despite the fact he never really became established as a regular with Chelsea between 1950 and 1955, Tottenham Hotspur paid £18,000 for his transfer in December 1955. Smith played for Brighton and Hove Albion from 1964 to 1965, scoring 19 goals in 31 appearances.
He played for England from 1961 to 1964, scoring 13 goals.
He died on 18 September 2010 following a short illness at a hospital in Enfield, London.