Born in West Bromwich, Parkes, nicknamed "Lofty" for his booming kicks upfield, joined Wolves in 1962 straight from school and turned professional two years later.
After several years in the reserve league, he made his first-team debut on 19 November 1966, saving a penalty in a 3–2 win over Preston North End.
Parkes anchored the team as it proceeded to win the USA title, defeating Washington Whips (represented by Aberdeen) in the final.
Parkes would return to the United States two years later, in a similar "guest" role, as Wolves represented Kansas City Spurs in the NASL's 1969 "mini-season."
The keeper won a UEFA Cup runners-up medal in 1972, after saving two penalties in the semi-final tie with Ferencváros to help the club to the final.