LONDON – If the United States didn’t exist, would Britain have had to invent it? That’s one of the passing meditations prompted by “Inventing America: A Year of American Culture,” the banner title for the Barbican Center’s 10-month immersion in virtually every American art form that began Jan. 25.In its American focus, the festival is operating on a scale the likes of which this country has rarely seen. It’s the brainchild of Barbican arts director Graham Sheffield, who puts the cost at £3 million ($4.86 million), within, he says, “10% either way.” Sheffield came to the job two years ago with, he recalls, “a blank sheet of paper” and an unusually hefty number of weeks to fill: His arrival coincided with the Royal Shakespeare Company’s decision to vacate the center’s two theaters over the summer period. Sheffield trawled the States for legit fare, catching “The Capeman” and “The Old Neighborhood” on his most recent circuit before Christmas. The result, at least in theater terms, is an eclectic mix that gathers under one roof aspects of the American stage seen in Britain before but inevitably in a more scattered form. The straight-play centerpiece is poised to be the import from Chicago’s Steppenwolf Theater of “The Man Who Came To Dinner,” starring John Mahoney (“Frasier”) and — in a return to the ensemble from which she had resigned — Glenne Headly. The intriguing director is James Burrows, TV series creator-director and, perhaps more pertinently, son of writer-director Abe Burrows (“How to Succeed in Business Without Really Trying”). The July 16-25 production marks Steppenwolf’s first London visit since “The Grapes of Wrath” played a brief stint at the National in 1989. “The Man Who Came to Dinner” opens in Chicago April 26, running through June 14: The same play was mostly panned in a Gene Saks-directed revival for the RSC in 1989 with a cast that included a then little-known Ralph Fiennes. Speaking from Chicago, Steppenwolf artistic director Martha Lavey told Variety, “There’s a certain cachet that attends moving our plays anywhere, especially to an exciting venue like the Barbican.” The theater will program a trip to London for Steppenwolf patrons, she adds. Elsewhere, Sheffield says he wasn’t necessarily seeking “15 totally new directors and choreographers nobody’s ever heard of. It seemed more sensible to us to go to reasonably familiar names who have a proven track record but to try to find them working in new directions.” New guises will be worn by Robert Wilson and Philip Glass in their cinema-flecked performance piece “Monsters of Grace,” coming May 19-23 directly from its L.A. premiere, and by Peter Sellars, who is working in Chinese with Tang Xianxu’s “Peony Pavilion,” scored by Tan Dun (Sept. 16-19). Seen in the studio-sized Pit Theater will be solo artists Lisa Kron, with “2.5 Minute Ride” (July 21-Aug. 1) and Roger Guenveur Smith with “A Huey P. Newton Story” (Oct. 6-17). David Feldshuh’s much-traveled 1989 play “Miss Evers’ Boys,” directed by Martin L. Platt, has its British premiere in the theater Sept. 16-Oct. 3. As for homegrown productions of American classics, the Marx Brothers’ “Animal Crackers” will be performed by Manchester’s Royal Exchange Theater in a mobile venue in the Barbican sculpture court.