Michael Dempsey (Michael Brandon) is a New York City cop who makes the Big Apple too hot to hold him. His superiors hand him over to the London Metropolitan Police, where he is teamed with Lady Harriet Makepeace (Glynis Barber). Hilarity ensues as they fight crime.
- Armed Blag: In "The Squeeze", a heavy duty transit van carrying half a million pounds in used notes is high jacked, drivers and all and S.I. 10 is tasked to find it.
- Belligerent Sexual Tension: Oh so much. The immediate antagonism between Dempsey and Makepeace was countered by a strong physical attraction. In fact, the tension was so palatable onscreen that Brandon and Barber married in real life in 1989, and have been together since. They even had a son together, Alex.
- The Boxing Episode: In "The Prizefighter", Dempsey and Makepeace find the broken body of a bare-knuckle prizefighter on the street carrying counterfeit money. Posing as an American couple named Dwayne and Lu, they manage to get into the illegal underground fight.
- Breaking Out the Boss: In "Hors de Combat", gang leader Frank Price is sprung out of jail, only to be killed by his accomplices.
- The Casino: In "Lucky Streak", Dempsey happens to be present at a casino when it is robbed and a security guard murdered.
- Catchphrase: 'Life is tough and then you die.' Or was it 'Life's a bitch and then you die'?
- Cowboy Cop: Dempsey, naturally. His actions making New York too hot for him are what get him sent on the 'exchange program' to the UK.
- Da Chief: The long-suffering Detective Superindendent Gordon Spikings has the unenviable task of dealing with Cowboy Cop Dempsey"Dempsey, when the prime minister and the home secretary instructed me to set up this special unit to combat major crime, I did not expect to be wet nursing ex-Vietnam soldiers toting bazookas!"
- Female Flatfoot and Snarky Guy: She's a competent but single London cop (who is also titled hereditary aristocracy), he's a cleaned-up Dirty Harry type from the NYPD who gets unexpectedly made her partner for reasons that are never mentioned again after the pilot episode.(After Lady Harriet Makepeace addresses Lt Dempsey with the English pronounciation "Lef-tenant")Dempsey: You know how to say "Lootenant", don'tcha? Just put your lips together and go "OO".
- Gentleman Detective: A female version, as DS Harry Makepeace is more properly Lady Harriet Makepeace.
- Government Agency of Fiction: SI10, which fulfils a similar role to CI5, though it has a more rigid hierarchy and appears to be an actual police unit.
- Opposites Attract: Virtually everything about the two lead characters is different, but that doesn't stop their ability to deal with the bad guys or the Belligerent Sexual Tension between them.
- Real Life Writes the Plot: after Dempsey orders a Budweiser in one episode a huge crate of beer arrived from the company in thanks. Afterwards the production crew made sure the character drank nothing else in the hope of obtaining more.
- Recruiting the Criminal: In "Bird of Prey", Dempsey and Makepeace have to get Dempsey's nemesis, Keith Lymon, out of prison and convince him to help find a young girl kidnapped by Eddie Dean.
- Serial Killer: In "Out of Darkness", SI10 is hunting for the so-called 'Thriller Killer', who kidnaps blue-eyed brunettes and kills them within 20 hours. But the killer takes an interest in Makepeace as she and Dempsey get close during their investigation and demands to meet with her one on one.
- Stalker with a Crush: In "Love You to Death", Dempsey is stalked by a homicidal women who obsesses over him, and who hates Makepeace for being with him.
- Wunza Plot: One's an American street smart loose cannon cowboy cop, one's a refined aristocratic proper young British police officer. Together they fight crime and make sparks fly between them!
- Ye Olde Butcherede Englishe: Dempsey finds Makepeace at an archery range and launches into a fake monologue full of butchered English before Makepeace tells him to "stop butchering the language".