Quixall was born in Sheffield, West Riding of Yorkshire. He started his career with Sheffield Wednesday. In 1958, after the Munich air disaster, he signed by Matt Busby for Manchester United. The signing was a then British record fee of £45,000. He won the FA Cup with Manchester United in the 1963–64 season. He later played for Oldham Athletic, Stockport County, Altrincham and Radcliffe Borough.