Brooke was born in Bethnal Green and began his career with Tottenham Hotspur. He spent a year on loan at Swedish side GAIS scoring eight goals in 23 appearances and made his Spurs debut in a 3–2 defeat against West Bromwich Albion. His full debut came in a 4–4 draw with Southampton with Brooke scoring twice. His debut season ended with a substitute appearance in the 1981 FA Cup Final which saw Tottenham beat Manchester City in a replay. His second season with Spurs saw the team again lift the FA Cup in a replay but Brooke's place in the side came under threat from Glenn Hoddle and Tony Galvin. He played 33 times in the 1982–83 season scoring nine goals but his run in the side was cut short due to a near fatal car crash in February 1983. It took him seven months to regain fitness and struggled to get back into the side due to his injuries causing him to be easily short of breath. He played in just seven matches in 1984–85 and was sold to Norwich City.