McQueen was a
goalkeeper (the position in which his father
Tom had played professionally) as a schoolboy but later switched to centre-back. He was signed at the age of 18 by
St Mirren from Ayrshire Junior team
Largs Thistle. He soon had scouts from other clubs monitoring his progress and it was
Leeds United who finally offered £30,000 (£ today) in the 1972 close season, seeing him as a long-term replacement for the ageing
Jack Charlton. Charlton played for some of the
1972–73 season but had decided to retire as the season was drawing to a close. McQueen played on six occasions in his first season at Leeds, including a
substitute appearance in the
1973 European Cup Winners' Cup final, which Leeds lost to
A.C. Milan. With Charlton retired and Madeley playing in many positions, McQueen was in the team for most of the
1973–74 season. Leeds won the
League Championship, with a run of 29 matches without a defeat from the start of the season with McQueen playing alongside
Norman Hunter as Leeds' first-choice centre back pairing. McQueen and Hunter excelled at the back the following season, notably in Leeds' campaign in the
European Cup, during which McQueen scored three goals. He was suspended for the
1975 European Cup Final after being sent off in the semi-final versus
Barcelona. Leeds went on to lose 2–0 in the final versus
Bayern Munich. He had declared only weeks earlier in
Shoot magazine that he wanted to stay at
Elland Road for his entire career. He played in the
1979 FA Cup Final against
Arsenal, scoring United's first of two goals in the 86th minute, but again finished on the losing side. McQueen finally gained an
FA Cup winner's medal in the
1983 FA Cup final, which United won after a replay versus
Brighton & Hove Albion. Earlier that season he was also in the team defeated by
Liverpool in the
League Cup final, He left
Old Trafford in the 1985 close season, having suffered from persistent knee injuries. ==International career==