Hapgood was born in Bristol and started his footballing career in the mid-1920s as an amateur playing in local football (while employed as a milkman), before getting his big break at Kettering Town in the Southern League. He was signed by Herbert Chapman's Arsenal for £950 in 1927. Initially a thin and fragile player, Arsenal's trainer Tom Whittaker forced him to take up weight training, and abandon his vegetarianism, and Hapgood eventually became known for his physique and power.