Set in the days when the most notorious bank robbers weren’t employed by banks, Michael Mann’s account of the rise and fall of John Herbert Dillinger (“Public Enemy Number 1” ©1933, J. Edgar Hoover) is by far his best film since Heat.

In many respects it is Heat, remade with Tommy guns, neater haircuts and no interruptions for coffee between the master criminal and his dogged pursuer.

Bearing all Mann’s trademarks – the style, the attention to detail, the fun-sapping seriousness - it follows Depp’s ultra-confident gangster from his parole in May 1933 (after nine years inside) to his well-documented demise outside a Chicago cinema on July 22, 1943.

Not much time to create a legend, then, but long enough for Dillinger to gain Robin Hood status in Depression-hit America. Public enemy? Hoover couldn’t have been more wrong (unless you count wearing ladies’ underwear but that’s another story).

“Who cares what the public thinks,” asks one of Dillinger’s boys when the boss airs his reservations about kidnapping. “I do. I hide out among ‘em.”

But, anxious to prove that his Bureau of Investigation should have its powers extended beyond state lines – thus making it federal – ambitious suit Hoover (a chunky Crudup) puts ace G-man Melvin Purvis (Bale) in charge of the Dillinger squad.

Under strict orders to play hardball and with experienced agents and cutting-edge wire-tap technology at his disposal, Purvis’s appointment is bad news for Dillinger.

Not only has he given himself an Achilles heel by falling for coat-check girl Billie Frechette (Cotillard), but his nervous money launderers have shut him out, forcing him to hook up with other high-profile desperados like loose cannon ‘Baby Face’ Nelson (Stephen Graham, This Is England’s chief yob) and kidnap specialist Alvin Karpis (the underused Giovanni Ribisi).

Suddenly, life at large isn't so much fun as Purvis and his boys close the net, picking off the gang and capturing Billie with law enforcement techniques both fair and foul.

Ultimately, the mobster's fate is decided by an old-fashioned hunch. The flatfoots know he'll be going to the movies, but which one: the Clark Gable flick or the wholesome family film? As the man says, “John Dillinger ain’t goin’ to a Shirley Temple movie.”

Mann sets his stall out early, hopping onto the running board from the get-go with Dillinger defying criminal convention by breaking into prison.

He certainly knows how to stage a shootout, and frequently does, though without quite reaching the bar he set himself in Heat.

Luckily, Depp is the perfect anti-hero, a screen-filling portrait of unaffected self-confidence and charisma. Cotillard, too, puts meat on her moll.

Elliott Noble