Burke was born in Nottingham, and came through the ranks at Nottingham Forest. His only first-team appearance was on 20 October 1976, while still a schoolboy aged 16 years 22 days, as a substitute in the Anglo-Scottish Cup against Ayr United. He moved on to Second Division club Queens Park Rangers in September 1979 for a fee of £125,000, and made his debut in the Football League on 7 September in a 3–0 win at home to Fulham. He played quite frequently at the beginning of his QPR career, and came on as substitute in the 1982 FA Cup Final replay, which QPR lost to Tottenham Hotspur. He had several loan spells towards the end of his QPR career – at Millwall from October to December 1983, at Notts County from October to December 1984, at Lincoln City from August to September 1985, and at Brentford from March to May 1986 – before leaving the club at the end of the 1985–86 season on a free transfer to Doncaster Rovers. He finished his League career with two seasons at Doncaster, including a loan spell at Stockport County. Burke's senior career finished in Non-League football, turning out for Shepshed Charterhouse and Grantham Town.