The greats of British comedy have had a spotty record as far as catching on in the United States. The Monty Python troupe made it, for sure. So did Peter Sellers. As did Dudley Moore, though more as a louche stunt-casting curiosity of Hollywood’s high cocaine era than as the versatile performer he’d been in the 60s on the BBC. Moore’s old TV partner, the magnificent Peter Cook, never made it here, enduring the indignity of a failed early-80s CBS sitcom in which he played that hoariest of English stereotypes, the starchy butler. Then there’s an entire class of first-rate Brit comics, from Morecambe and Wise to Reeves and Mortimer, who have, by choice, remained strictly British phenomena, content never to hustle their talents beyond Blighty.

Steve Coogan would not mind conquering America. He is, by some distance, the most gifted comic performer to have come out of Britain in the last 20 years. But, somehow, he hasn’t connected in the U.S. the way Sacha Baron Cohen has with Borat, Ricky Gervais has with The Office, and Russell Brand has via his MTV appearances and his short-lived strategic marital alliance with Katy Perry.

“The kind of following I have in the U.S. is largely people who really like the very esoteric, Anglicized nature of what I’m doing,” Coogan says, roosting in the very esoteric, Anglicized workroom he keeps in his home just outside the seaside town of Brighton. There is a poster on the wall for Michael Caine’s 1966 Swinging London classic, Alfie, and on a bookshelf sit collectible Corgi models of James Bond’s Aston Martin DB5 from Goldfinger and Simon Templar’s Volvo P1800 from The Saint.

“Which, of course, stops me from breaking America,” he continues. “I do get recognized sometimes, but mostly”—and here he casts his eyes downward in pantomime dejection—“in Manhattan and in vinyl-record shops.”

Outside of this discerning boutique audience, Coogan registers on these shores as a character actor: the guy who played Octavius, the Roman-warrior pal to Owen Wilson’s cowboy, in the Night at the Museum movies, as well as Larry David’s incompetent shrink in Curb Your Enthusiasm, the white-collar heel pursued by Will Ferrell and Mark Wahlberg in The Other Guys, the harried director of the film-within-the-film in Ben Stiller’s Tropic Thunder, and the pompous brother-in-law to Paul Rudd’s title character in Our Idiot Brother.

Fine as they are, these performances provide little insight into what all the fuss is about when people fuss about Coogan. His reputation really rests upon a body of British TV work with which few Americans are familiar—in particular those programs in which he plays his most celebrated creation, a boorish, hopelessly square talk-show host named Alan Partridge.

“I first saw Steve doing Alan Partridge on TV when I was in London to do a play in ’99,” says Rudd, an American of British parentage. “It just killed me. It was so nuanced and so broad at the same time—and so funny.”

“Every American comic knows who Steve is, whether it’s Stiller or Ferrell or Jack Black or me, and the way we all discovered him is through the Partridge DVDs,” says Adam McKay, who directed The Other Guys and is Ferrell’s frequent co-conspirator, with Talladega Nights, Anchorman, and the Web site Funny or Die to his name. “And everyone watching those DVDs had the same reaction,” McKay says. “How did I not know about this guy?”

The good news is that Coogan may be poised, at the age of 46, to at last get his due—if not as a bona fide movie star, then at least as the pan-Anglophonic titan of comedy that he deserves to be. There was an intimation of this last year, when a clip of him and the Welsh comedian Rob Brydon trading Michael Caine impressions in a restaurant—“Yerronly supposed to blow the bloody doors off!”—became a viral sensation on both sides of the Atlantic. The Trip, the six-episode BBC program from which the clip was taken, won Coogan the warmest reviews he’d had in years, prompting its release last summer, in edited-down form, in U.S. movie theaters.