There are a couple of fine performances—which are also fine impressions—at the center of this period drama loosely based on the behind-the-scenes dramatics during the filming of “The Prince and the Showgirl,” a mediocre Ruritanian bedroom comedy, on an English soundstage in 1957. Michelle Williams makes an excellent Marilyn Monroe, the star of the picture, catching the fragile actress’ combination of shrewd calculation and kewpie-doll vulnerability with skill. And Kenneth Branagh is a match for her as Laurence Olivier, the nervous producer of the movie as well as Marilyn’s autocratic director and insecure co-star.

If “My Week With Marilyn” is any indication, the making of “The Prince and the Showgirl” was far more interesting than the picture itself turned out to be. According to the screenplay, based on a memoir by Clive Clark, who was the young, inexperienced third assistant director (or glorified go-fer) on the project, Olivier, desperate to revive a flagging career, had cast the blonde bombshell for her superstar status and irresistible audience draw (irritating his wife Vivien Leigh—here Julia Ormond—who’d played the part onstage). But with her insecurity, emotional fragility and devotion to ‘method’ acting—she was accompanied (and supported) during the filming by the fawning Paula Strasberg (Zoe Wanamaker), wife of the legendary Lee—the casting insured a clash with Olivier, who was the craftsman par excellence, accustomed to professionalism and technical perfection above all. And though their co-star Sybil Thorndike (a delightful Judi Dench) tries to smooth things out between them, her efforts are in vain.

Of course the whole story is told through the prism of Clark’s recollections, which puts much of the spotlight on him. As played by Eddie Redmayne—who’s engaging enough but compared to the stars a mite colorless (a romantic fling with a local waitress played by Emma Watson is rather a boring plot thread)—he becomes a pivotal confidante (and wide-eyed companion) to Monroe, especially after her new hubby Arthur Miller (Dougray Scott), nondescript) decamps for America. Clark, a scion of an upper-crust family longing to get into cinema production, not only ferries her around to his old school (where they mobbed by current students) and a royal residence (where the keeper—a relative of his almost inevitably played by Derek Jacobi, the new king of cameos—shows off his library), but skinny-dips with her and acts as her comforter when she has a bad night. Of course Clark—and scripter Adrian Hodges—are too gentlemanly to suggest that the young fellow’s relationship with the actress went beyond the platonic, though they portray her manager (Dominic Cooper) as irritated by it. And eventually the film-within-a-film was finished—and even Olivier has to admit that Monroe, despite all the problems on-set, is a magnetic screen presence who puts his fuddy-duddy theatrical technique to shame.

Simon Curtis, whose work has until now been largely in television, directs in a solid but rather stolid “Masterpiece Theatre” vein. But his approach, which unimaginative (as Olivier’s was in “The Prince and the Showgirl”), certainly allows the exquisite period work of the behind-the-scenes crew (production designer Donal Woods, art director Charmian Adams, set decorator Judy Farr and costume designer Jill Taylor) to shine, especially in Ben Smiithard’s glossy widescreen cinematography.

And he gives his leads room to blossom. Williams might not be the spitting image of the pouty Monroe, but she comes close physically, and certainly embodies her emotionally. It’s a stunning performance than goes well beyond impersonation. In her shadow Branagh might not get the recognition he deserves. But he’s great as well, tossing off Olivier’s inflections with practiced aplomb. (Of course his skill shouldn’t be all that surprising: he did an amusing caricature of Woody Allen in “Celebrity,” too, but that was a terrible movie.)

“My Week With Marilyn” may not be one for the ages—neither was “The Prince and the Showgirl,” after all. But especially for film buffs, it’s an entertaining filling-out of an intriguing footnote of cinema history. And one can’t blame it for not having the enrapturing quality of one of Marilyn’s actual performances in, say, “Some Like It Hot.” As it turns out, Monroe once removed is better than none.