Will Hay plays Sergeant Samuel Dudfoot, an inept policeman, stagnating in the sleepy village of Turnbotham Round (pronounced Turnbottom), where there has been no crime for a decade. After the Chief Constable tells them that there is not enough local criminal activity to justify their station's existence, three incompetent policemen decide to start manufacturing crimes to "fiddle the figures". Dudfoot, together with Albert Brown (Graham Moffatt) and Jerry Harbottle (Moore Marriott) create a crime wave by framing motorists in a speed trap and concocting false evidence.
They also leave a keg of whisky unattended in order to frame someone as a smuggler - and then accidentally discover a real smuggling ring!
Sergeant Dudfoot talking about his life as a policeman at Turnbotham Round during a radio broadcast. His staff Albert and Harbottle (played by Graham Moffatt and Moore Marriott) enter after they have been poaching and Harbottle ruins the broadcast.
The next day, Dudfoot receives a letter from the Chief Constable. The letter states that an investigation will shortly take place to see if the police force in Turnbotham Round is necessary at all since no arrests have been made in the ten years that Dudfoot has been a policeman. Dudfoot decides to set a speed trap and stops passing cars down a country lane just outside the village. After stopping and later releasing a man who has neither a license nor insurance, Dudfoot, Harbottle and Albert stop, question and knock out another driver who is actually the Chief Constable. They drive the unconscious Chief Constable back to the police station and lock him in the cell. Dudfoot then drives the Chief Constable's car into Harbottle's shop window to create the impression that the Chief Constable had just had an accident. However, when the Chief Constable comes round, he fails to be fooled by the 'accident', but the Squire intervenes and claims to have witnessed the accident, which saves Dudfoot, Harbottle and Albert from a lot of trouble.
The Chief leaves after Harbottle makes up a story about a Headless Horseman when questioned about his old looks. Dudfoot states that they need to arrest a criminal soon or else their police station will be closed down and Harbottle takes him to the library to look for books on crime. On their way the coastguard stops them and tells them his brother a lighthouse keeper wants a light hung up on top of the police station as his grandmother is very ill and he agreed to the idea that if he could see the light on the Police Station tower he'd know his grandmother was still alive. (Harbottle misunderstands this, thinking that the grandmother is alone in the lighthouse, causing him to sob uncontrollably whenever the matter is mentioned.) Unknown to the cops, this is connected to the smugglers.
Later Albert suggests that they should capture some smugglers by placing a keg of brandy on the beach and getting a witness to see what happens. Dudfoot comes back into the station with a fisherman, who is carrying a keg of brandy and Albert and Harbottle say they haven't taken their keg down to the beach yet, therefore resulting in two kegs of liquor.
Albert’s girlfriend Emily screams and passes out as she claims to have seen a Headless Horseman. Later Albert spots the Headless Horseman too and after an encounter with him in the Squire’s garage, they are scared off by the Horseman, though Harbottle finds a small package which he tucks away.
Back at the police station, the Chief Constable phones them about the smuggling and instructs them to find the navigational light the smugglers are using. In spite of the light episode with the coastguard, the three policemen brush off the idea that the coastguard is involved with smuggling. A warning note to keep their noses out of things that are not of their concern is wrapped around a stone thrown in through the police station window.
A ticking sound is heard from the package that Harbottle earlier picked up and they find pocket watches inside. Harbottle then recites a rhyme which tells the legend of the Headless Horseman, although he doesn't know the last line, but his father does. So the trio decide to pay him a visit. Harbottle's father reveals the line thus also revealing the place, the Devil's Cave where the smuggling is taking place.
The trio investigate the cave, follow a tunnel and discover many barrels of liquor and other things that seemed to belong to Harbottle. They eventually discover that they are in their own cellar. They decide to call the Chief Constable, but are confronted by the Squire who reveals that he is the leader of the smugglers. After a fight in the dark, the smugglers lock the trio in their own cell and escape, deciding to give chase in their car, but since the other police agents think they are smugglers as well, their car is also wanted.
After a chase, the police agents finally capture the smugglers. The Chief Constable asks the Squire if he has seen him before, but the Squire denies this. Dudfoot then reveals the story of the accident at Harbottle's shop, and the Chief Constable orders that the trio be arrested. Dudfoot punches the Chief Constable and the trio run as fast as they can along the race track away from the other pursuing policemen.Will Hay - Sergeant Samuel Dudfoot
Graham Moffatt - Albert Brown
Moore Marriott - Jerry Harbottle/Harbottle Senior
Glennis Lorimer - Emily Martin
Peter Gawthorne - Chief Constable
Charles Oliver - The Squire
Herbert Lomas - The Coastguard
Dave O'Toole - Dudfoot's witness
Noel Dainton - Revenue Officer
Cyril Chamberlain - (uncredited) Radio Announcer
Brian Worth - Broadcasting Engineer
Patrick Aherne - First motorist
Desmond Llewelyn - (uncredited) "headless horsemen".
In 1982, comedy duo Cannon and Ball filmed a loose remake of Ask A Policeman, titled The Boys in Blue. Though not a remake, 2007's Hot Fuzz borrowed the plot device of policemen uncovering organised crime in a sleepy area of rural England.