Smith was an integral part of Bill Nicholson's famous double winning Tottenham team of 1960–61. He was Tottenham's top scorer in the double-winning season, with 33 goals scored in 43 games, including in the first of the two goals in the 1961 FA Cup Final. The team also went on to retain the FA Cup in 1962 (scoring in the Final again) and win the 1963 UEFA Cup Winners' Cup. He is one of Spurs' all-time top goal scorers, third behind Harry Kane to Jimmy Greaves, with 208 goals scored in 317 senior matches, including 12 hat-tricks.