Cinema’s police officers it’s probably best not to call in.

This Friday sees the release of Mr Martin McDonagh’s Three Billboards Outside Ebbing, Missouri, cinema’s latest excursion into policeman behaving very badly. But who are the real dirty cops of cinema? Here are MR PORTER’s filthiest five.

Directed by Mr Curtis Hanson, starring Messrs Russell Crowe, Guy Pearce, Kevin Spacey and James Cromwell

If you fancy a weekend of self-induced purgatory, draw the blinds, charge a tumbler and subject yourself to the many, many films that have manfully tried – and dismally failed – to channel Chinatown, Mr Roman Polanski’s sunlit noir of vice and corruption in the City of Fallen Angels. There are a lot of them.

LA Confidential is different, though. Yes, it owes much to Chinatown. But, in many ways, it surpasses its ancestor. The then unknown Mr Russell Crowe is the quiet bruiser with a thing for helping women. The equally unknown Mr Guy Pearce is the clean-shaven career guy, unafraid to rat on fellow officers if it means getting ahead. Then there’s Mr James Cromwell, the crumple-shirted, whispery-voiced vet who seems to sweat coffee and cigarettes. And Mr Kevin Spacey, the droll, witty cop with the flashy suits and the sideline in arresting celebrities for the gutter press. Each is dirty, but who will catch who? A film that belongs in the canon of classic Hollywood.

Directed by Mr Michael Winterbottom, starring Mr Casey Affleck

“Everyone thinks they know you, just because they grew up with you.” So says Mr Casey Affleck’s Lou Ford, a folksy, elegantly polite Texan sheriff. It’s the 1950s in the Deep South, and Lou, behind his married, respectable facade, is secretly surrendering himself to the fantastic passion of violence.

He’s having an affair with a prostitute with a masochistic streak. And so, bit by bit, he gives in to the craving, raging thirst within him.

The film is shot, sometimes jarringly, by the shape-shifting British director Mr Michael Winterbottom. In his hands, it veers between sensational and salacious to lurid and queasy to icy cool in its detachment and remove.

There is no evasion here, no affectation or explaining away, no sexing-up or toning-down. The prodigious Mr Affleck lurks at the film’s centre, vulnerable as a child as he succumbs to evil – yet capable, somehow, of almost eliciting our sympathy.

Directed by Mr Werner Herzog, starring Mr Nicolas Cage

Lieutenant Terence McDonagh is a hero. A detective in post-Katrina New Orleans who has saved a drowning prisoner, he is now tasked with investigating the killing of five Senegalese immigrants by a local kingpin. But he’s hooked on pipes, and happy to dip into the supply. The film is based on the Mr Abel Ferrara original, a sleazy, low-budget pulp-punk shocker, with a young(ish) Mr Harvey Keitel as a disintegrating NYPD cop. Reprising this, Mr Nick Cage has never been better, his half-crazed, equine-faced histrionics finding an unlikely ally in Mr Werner Herzog’s satirical love of the bizarre, depraved and macabre.

Directed by Mr William Friedkin, starring Mr Matthew McConaughey

Detective Joe Cooper of the Dallas Police Department (played by Mr Matthew McConaughey) cruises through a Texan trailer park in an unmarked car. He’s there to keep the peace, but he has “a little business on the side” – that is, a sideline in contract killing. It’s worth saying here that this film made its debut in the dark days before the McConaissance, when our leading man was enriching cinema with the likes of Ghosts Of Girlfriends Past and How To Lose A Guy In 10 Days. Fans of those films likely weren’t ready for the lustful, malevolent devil of Joe, but that doesn’t mean we can’t enjoy him now. The then-76-year-old director Mr William Friedkin, of 1970s classics The Exorcist and The French Connection, brings his quasi-ironic lightness of touch here, as Joe doles out some of the most gruesome scenes in modern cinema. Not one to watch with a bucket of fried chicken.

Directed by Mr Oren Moverman, starring Mr Woody Harrelson

No pretending here. No pretence of playing it straight. The co-writer, modern noir godfather Mr James Ellroy, treats us to an implacably filthy LAPD officer. Mr Woody Harrelson plays Detective David Brown with a glowering, sweating, boiled egg of a head as he cruises through the bleached-out, smog-tinged streets of South Central. In Dave’s defence, he doesn’t discriminate – he just loathes everyone. He lives with his two ex-wives, who happen to be sisters. They hate him, yet he isn’t above begging for sex. The monster that he is, his lingering, pleading humanity always makes them give in.

Three Billboards Outside Ebbing, Missouri is released 12 January

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