Swift broke into the Manchester City first team in 1933, taking part in the club's run to the 1934 FA Cup Final, where the club triumphed 2–1 against Portsmouth. Three years later Swift won a League Championship medal, after playing in every match of Manchester City's championship-winning season. War denied Swift several years of playing in his prime, though during wartime he was chosen to represent his country in international matches. After the war he made his competitive international debut, playing 19 internationals between 1946 and 1949.