Edinburgh was born in Basildon. He started his playing career at Southend United in 1988. He was loaned to Tottenham Hotspur in 1990 and signed a contract with the club that same year. During his time at Totteham between 1990 and 2000, Edinburgh made 258 appearances for the club and scored once. He also won two trophies with Spurs, the 1990–91 FA Cup and the 1998–99 Football League Cup. He signed for Portsmouth in 2000. He left the club in 2003 to become player-manager of Billericay Town.