Watch the short PSA Have You Got Your License Yet?, that was released in 1923.
The BBC began radio broadcasts on 14 November 1922, and less than a year later they were issuing thinly-veiled threats to "pirates" who hadn't paid their licence fee, via the Topical Budget newsreel of 29 October 1923. Presumably the humiliation of being depicted as a chimpanzee was enough to persuade miscreants to pay up - later campaigns would resort to far more direct threats, such as the eternally roving detector van with its postcode database, neither of which had been invented by 1923.