Mullen joined the Midlanders in June 1937, turned professional on his 17th birthday, and remained with the club until his retirement in May 1960. His league debut came in February 1939, in a 4–1 win over Leeds United. He made 488 appearances in total, scoring 112 goals, helping the club win their only three league titles (1953–54, 1957–58 and 1958–59) as well as the FA Cup in 1949.