Moffatt was born on 6 December 1919 in Hammersmith, West London (England). He first worked as a call boy at Shepherd's Bush Studios, until actor Tom Walls suggested him for a bit part in the 1934 film A Cup of Kindness. Moffatt appeared in five more films, in mostly uncredited, minor roles, before getting his big break in Will Hay's Where There's Will (1936), then going on to appear in many more of Hay's films, alongside Moore Marriott.