In a live radio broadcast from the coastal village of Turn-Botham Round, Police Sergeant Dudfoot is interviewed regarding the remarkable fact that there has been no recorded crime there in the entire ten years that he has been in charge. The authorities wonder if the station is necessary and propose to close it down.

Dudfoot and his assistants, Constables Albert and Harbottle, set about manufacturing some criminal activity to save their jobs, setting up a trap on a stretch of country road to catch motorists and charge them with speeding. An innocent driver who argues with them is knocked unconscious and taken back to the station where it is discovered that he is the Chief Constable. Before he recovers consciousness, Dudfoot drives his car into a village shop front. They then claim that the Chief Constable had an accident driving through the village and the local squire helps them out by insisting that he saw it happen. The baffled Chief Constable departs.

In a further attempt to concoct evidence of crime, the trio decide to place a keg of brandy on the beach to suggest that smuggling is taking place. Dudfoot finds a real keg of rum and Albert's girlfriend is terrified by the sight of a flaming hearse with a headless horseman. The three policemen see the phantom hearse for themselves and follow it into the squire's garage where Albert pockets a package lying on the floor. They run off after being frightened by the headless horseman.

The Chief Constable telephones with information that real smuggling is going on with the help of a guiding light that Dudfoot soon realises is the one he has permitted a local to hang in the tower of the police station. Harbottle's bedridden father remembers the last line of an old rhyme about the headless horseman, which leads the trio to investigate an old cave at the foot of the cliff. There they find kegs of liquor and a tunnel leading up to a room full of contraband that they eventually recognise as the cellar of the police station.

The squire interrupts their attempt to report the find to the Chief Constable, reveals that he is the head of the smuggling ring, and locks them up in the police station cell after handcuffing them together. They escape, still attached to each other, and leap into their police car to chase after the squire who is fleeing in a lorry full of contraband.

Believing that it is Dudfoot, Albert and Harbottle who have been carrying out the smuggling, the Chief Constable is hot on their track. The trio exchange their police car for a mobile roadside café, then take over a London Transport bus in their pursuit of the squire's lorry. Gaining passengers whenever the bus is forced to stop, they follow the lorry onto the racetrack at Brooklands where cars are flashing past.

Going around the circular course in opposite directions, the bus and the lorry crash into each other. The Chief Constable arrives. Although the squire is exposed as the real villain, Dudfoot, Albert and Harbottle are not forgiven for their past demeanours and run off round the track to escape arrest.