Born in Eastwood, Nottinghamshire, Woodcock had trained with Alan and Steve Buckley as a child, coached by their father, and had played for Priory Celtic. He started his career at Nottingham Forest, signing a contract in January 1974. After loan spells at Lincoln City and Doncaster Rovers, Woodcock broke into the Forest first team in 1976–77, helping the team to promotion to the First Division. Woodcock would later credit the Lincoln move and the leadership of Graham Taylor as being instrumental to his development. Under Brian Clough, Forest went on to win the First Division title and Football League Cup in 1978 with Woodcock winning the PFA Young Player of the Year award that year as well, and the European Cup in 1979. He also scored in Forest's victory over Southampton in the 1979 Football League Cup Final.