The chase film was a popular genre during the era this chase film "The Unfortunate Policeman" was released. The genre began in Britain as films about criminals being chased, such as in James Williamson's "Stop Thief!" (1901), as well as in "Daring Daylight Robbery" and "Desperate Poaching Affray" (both 1903). The comedy chase, it seems, began in America with "Personal" (1904). Back in the UK, here is Paul's Animatograph Works's contribution to the genre. In turn, its involvement of a policeman in the chase and as the butt of the joke makes it a forerunner to such Pathé and Keystone comedy chases, as well as those by Buster Keaton.
"The Unfortunate Policeman" isn't very funny today, but it's historically interesting. As with the other aforementioned chase films, it is well edited. Furthermore, the genre was instrumental in the development of continuity editing and the story film. This can also be seen in some of the more famous films that are essentially an offshoot of the chase films, such as "The Great Train Robbery" (1903) and "Rescued by Rover" (1905), both of which display similar chase structures and the criminal elements of the earlier chase films. The framing and continuity structure of "The Unfortunate Policeman" is especially similar to "Personal". In both films, shots begin with the characters a considerable distance from the camera, which they then approach and pass, with each stationary shot lasting on the screen until every character exits the frame.
On another point of continuity, the transition between the studio set in the first scene of what is in the film's story the exterior of the Jeweler's shop to the exterior shots on London streets is seamless--because Paul, like everyone then, used a naturally lighted stage. I've often criticized films where the shadows from these sets make it obvious that scenes aren't from within a character's home or some other structure with a ceiling and four walls, but the same vein of criticism can be applied to later films which pretend outdoor scenes but of which actually and obviously take place in an indoor, artificially-lit set.