Criminal Investigation Department

The Criminal Investigation Department, (PROSE: Dominion) or CID, was a branch of police whose detectives wore "plain clothes". (TV: The Hungry Earth) Though not strictly speaking uniformed, they were typically well-dressed, (PROSE: The Hollow Men) frequently wearing ties. (PROSE: Cat's Cradle: Warhead)

Gwen Cooper at least claimed to be a CID agent; at the time that she left her police job in 2007, the Department was investigating the Suzie Costello Life Knife murders. One of the CID officers showed her a diagram of the knife, which eventually caused her memories of Torchwood Three to come back. (TV: Everything Changes)

Brighton had such a department, whose staff included Detective Inspector Bob Lines. (PROSE: Missing, Part One: Business as Usual) Trey Korte pretended to be CID, but was actually just a psychic who helped out the police with false credentials. (PROSE: Instruments of Darkness)

When Rory Williams walked out of the TARDIS — disguised as a police box — in 2020 to Ambrose Northover, she figured he must have been CID because of his lack of uniform. (TV: The Hungry Earth)