Dyson was spotted playing football for the British Army during National Service After being demobbed in 1955 he joined Tottenham Hotspur from non-league Scarborough. Dyson played his first match for Tottenham against Sheffield United in March 1955. He played for the North London club until 1965. He was a regular member of the Double-winning side of 1960–61, scoring in the FA Cup Final against Leicester. Dyson was also a member of the team that won the 1962–63 European Cup Winners' Cup, scoring twice in the final against Atlético Madrid. He made a total of 209 appearances and scored 55 goals for Tottenham.