McCue was born in Stoke-on-Trent and was spotted playing for Longton schools and joined Stoke's ground-staff as an amateur in 1937. He signed professional forms in 1940 and due to his wartime occupation as a physical training instructor he remained local and made the left back spot his own from 1942–43 onwards, missing only one game from February 1943 to May 1945. The left-footed McCue's style was uncompromising, described as a 'grand kicker of the ball' and should an opposing winger get the better of him he would not averse the odd kick or two to rectify the situation. This earned him the nickname 'chopper' amongst his Stoke teammates. His impetuous tackling did lead to mistakes and a one such occasion McCue slipped as the attempted to tackle Sheffield United's Walter Rickett on the final day of the 1946–47 season, Stoke lost 2–1 and missed out on their first league title. After being demobbed, McCue played as a part-time professional working for the British Coal Corporation as a PT instructor. He trained intensely on a Tuesday's and Thursday's and his regimes were very army orientated. By 1948 Stoke's team-spirit was beginning to fall apart, with the loss of the title in 1947 and the departure of Stanley Matthews coupled with a number of big-name transfer failings caused rumbles of discontent with manager Bob McGrory. McCue along with five other players handed in transfer requests, each of which was rejected but the downward spiral continued which led to Stoke being relegated in 1952–53. Under new manager Frank Taylor McCue retained his famous consistency as the remained a vital part of the "Potters" team for seven seasons in the Second Division. He eventually gave way to the younger Tony Allen and ended his 23-year association with Stoke City in 1960 joining Oldham Athletic at the age of 35. By the time he left Stoke McCue had set a club record of appearances of 542 with 675 including war time appearances. But War League matches are considered unofficial and therefore he lies 2nd on Stoke's all-time appearance list. He ended his career with Fourth Division Oldham Athletic making 64 appearances under "Latics" manager Jack Rowley.
