“Their Finest “ is a movie about making a movie, specifically a glossy propaganda film meant to bolster morale in Britain in the darkest days of the second World War.

It is also very much a movie-movie. Good-looking, finely acted, and well-told, director Lone Scherfig (“An Education”) has made a charming, witty and romantic gem. It is “Shakespeare in Love” in World War II.

Adapted by Gaby Chiappe from the novel “Their Finest Hour and a Half” by Lissa Evans, “Their Finest” is centered on Catrin Cole (a luminous Gemma Arterton), a copywriter hired by the government to help write the “slop,” or female dialogue, for a film meant to lift the spirits of a war weary citizenry. She’s a sort of proto-Peggy Olson whose talents and thick skin get her a place at the table alongside the men (although she is, they make sure to hammer home, paid less than her male counterparts).

Catrin takes the job out of necessity — her husband Ellis (Jack Huston) is a disabled and temperamental artist whose bleak industrial landscapes aren’t selling and thus not bringing in any money for their rent. Although Ellis tries to talk her out of the work, Catrin comes alive in the writer’s room, sparring with the egotistical lead writer Tom Buckley (Sam Claflin) as they try to meld minds to make a compelling story out of a newspaper account of twin sisters who stole their alcoholic father’s boat to rescue soldiers from Dunkirk.

It’s a relentlessly appealing take on the creative process, laced with humor and insight as Tom and Catrin bicker and banter about just who the hero should be (a man or the woman?), and how strictly they should adhere to the facts .

What ends up being put into production, of course, is worlds away from reality, but there’s a lovely discovery of the truth at the heart of the sisters’ heroics that eventually makes it onto the screen.

Scherfig packs the film with fun side characters and pseudo showbiz insider jokes, like when they go out to the past-his-prime actor Ambrose Hilliard (Bill Nighy, always the scene stealer) for the “corpse role” of the drunken father who’s described as being a “shipwreck of a man” who is in his 60s but “looks older.” Ambrose, of course, thinks he’s being considered for the part of the hero and is stunned to realize otherwise.

They’re also, late in the game, instructed that they have to cast an American in the film because, in addition to British propaganda, the government now needs this film to persuade the U.S. to help out with the war efforts.

But just because some of the beats are predictable doesn’t mean that “Their Finest” is ineffective — quite the opposite. The elegantly composed script even begins to mirror the film within the film as the romantic tension grows between Catrin and Tom.

Without giving too much away, there is a beat (you’ll know it when it comes) that might sour things for some audiences, but it’s not enough to destroy all the good that’s there. Inspiring, funny and genuinely romantic, “Their Finest” is a solid, refreshing crowd-pleaser.