Leeds football club offered McQueen £30,000 in 1973. McQueen was in the team for most of the 1973-74 season. Leeds won the League Championship, going 29 games without defeat at the start of the season, and McQueen played a crucial part as Norman Hunter's defensive partner. At the end of the season, McQueen was called up to the Scotland squad for his debut against Belgium.
McQueen and Hunter excelled at the back the following season, notably in Leeds' campaign in the European Cup, during which McQueen scored three goals. McQueen was now a regular for Scotland; he was in the 1978 World Cup squad in Argentina but did not play due to injury, and played his last match for Scotland in 1981, attaining 30 caps and scoring 5 goals for his country.
In February 1978, McQueen moved from Leeds to rivals Manchester United for £495,000. McQueen helped Manchester United reach the FA Cup final in 1979, scoring a late goal as Manchester United came back from 2-0 down against Arsenal to level the scores, only for their opponents to wrestle the Cup back with a last-minute winner. McQueen finally gained an FA Cup winner's medal in 1983 after a replay against Brighton and Hove Albion.
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