A newly minted screenwriter named Catrin Cole learns how England’s cinematic sausage is made in the World War II drama “Their Finest.” In the writers’ room, true-life stories are stretched into fantasies, stock characters help gin up the drama, and all notions of subtlety are instantly shot down. It isn’t glamorous or artistic, but it sure is fun, and by the end of “Their Finest,” Catrin will have helped create something magical: an honest-to-goodness movie.

If “Their Finest” had taken this same approach to filmmaking, it might have had more magic of its own. Despite the solid cast, convincing details and interesting backdrop — Britain’s cinematic propaganda efforts — “Their Finest” is a faltering and underwhelming drama. Its chief problem is that it wants its characters and situations to seem believable, when what they should be is compelling. Time and again, “Their Finest” refuses to whip things up to give us a satisfying movie experience.

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Initially, the movie seems like a salute to wartime working women. Budding writer Catrin (Gemma Arterton) is hired by the Ministry of Information to churn out what screenwriter Tom Buckley (Sam Claflin) calls “slop” — dialogue that appeals to women. Catrin doesn’t object because the job pays and she’s living with a starving artist, Ellis (Jack Huston). Also, she and Buckley hit it off (despite his snobbery and chauvinism). It’s hard to see where Catrin will find a sense of empowerment in this particular love triangle.

Things liven up whenever Catrin is on the set of her film, “The Nancy Starling,” about two heroic women on a boat. It’s a skin-of-its-teeth production with charmingly creaky sets, low-budget effects (Dunkirk is a painting) and such endearing personalities as aging diva Ambrose Hilliard (Bill Nighy) and talentless American actor Carl Lundbeck (a deadpan Jake Lacy). When these folks disappear and Catrin goes back to wavering between a flawed artist and a chilly screenwriter, “Their Finest” grinds to a halt.

When this movie finally does throw in a bit of swooning tragedy, it’s so sudden and contrived that it feels almost like parody. Directed by Lone Scherfig and written by Gaby Chiappe (from a novel by Lissa Evans), “Their Finest” is a professional-looking but ultimately unengaging film. “The Nancy Starling” seems like a lot more fun.