Sedgley was born in Enfield. He made more than 180 first-team appearances for Tottenham Hotspur as a player after a £750,000 move from Coventry City in July 1989 before switching to Ipswich Town for £1 million in June 1994. More than 100 appearances followed for Ipswich before the final move of his playing career, a £500,000 transfer to Wolverhampton Wanderers in July 1997, where he again made more than 100 League appearances before retiring from the game in December 2000. He has two FA Cup-winners' medals. The first came with Coventry, as an unused substitute in the 3–2 defeat of Spurs in the 1987 final. He received his second in 1991 when Spurs beat Nottingham Forest 2–1.