 Having signed for Wolves on Boxing Day in 1964, Wagstaffe went on to play 404 league and cup games for the club, placing him in the top 15 all-time appearance makers for Wolves.Although not a prolific goal scorer, he won Match of the Day's goal of the month in 1971 for a 35-yard shot as Wolves went on to beat Arsenal 5–1, as well as scoring in the second leg of the UEFA Cup Final against Tottenham Hotspur the same year.Wagstaffe featured in the Wolves side that were competing in the United States of America in the inaugural United Soccer Association league as Los Angeles Wolves in 1967.