Carry on Constable (1960) on Netflix

With a flu epidemic running rife, three new bumbling recruits are assigned to Inspector Mills police station. With help from Special Constable Gorse, they manage to totally wreck the operations of the police force and let plenty of criminals get away, even before they arrive at the station. They all have to prove themselves or else they'll be out of a job and Sergeant Wilkins will be transferred. Sub-plots include romances between Wilkins and Moon, Constable and Passworthy.