Judi Dench rivals fish and chips for iconic Britishness. The reputation passed parody years ago with back-to-back Oscar nominations for playing the queen herself, twice. In “Mrs. Henderson Presents,” directed by Stephen Frears, Dame Judi puts a wicked spin on all this dignity as a wealthy widow who starts a nude revue in 1930’s London.

Ms. Dench’s comic take on aristocratic whimsy is sharp and winningly nutty. Sadly, it is cut short by the film’s precipitous nosedive into one of the sillier appeals to patriotism in some time. At his best (“The Grifters,” “High Fidelity”), Mr. Frears is an efficient storyteller. Here, he has created a sprightly entertainment, then packed up and left in the middle, forcing this creampuff of a film to fend for itself against World War II.

Mrs. Henderson runs her Soho theater with the help of producer Vivian Van Damm (Bob Hoskins), who concocts a successful brand of vaudevillian fusion. It is only when competing theaters rip them off that Mrs. H. proposes a very novel routine. The buttoned-up government official (Christopher Guest) who dispenses play licenses (the “Lord Chamber lain”) sets the ground rule: Any exposed women must remain still as paintings in a museum.

And so the jazzy spectacles begin: Singers cavort around tasteful nudes posed inside picture frames, on pedestals like statues, or as part of a giant harp. The crowd goes wild (and begins to skew male). Van Damm and Mrs. Henderson spar playfully, and there’s the guilty pleasure of watching someone rich enough to say whatever she wants.

An idea or two about art, sex, and power even germinates in all this. One woman observes that not even her boyfriend has seen her without clothes. And Mrs. Henderson and Van Damm assure the whole lot that it’s for their own good because they’d be jobless and starving otherwise.

Then the bombing begins, in every sense of the word. The theater remains open to bolster little England’s spirit, which is nice. But, alas, Henderson urges a showgirl to date a soldier. Within minutes the poor girl gets pregnant and dies in an air raid. Then we see Van Damm – the target of much of Mrs. Henderson’s merriment for hiding his Jewishness – weeping silently over headlines of purges in Holland, where his relatives lived.

“You live in your own world, Mrs. Henderson!” scolds the preggers showgirl. She’s right, and that’s what tanks the drama. Ms. Dench’s character is effectively detached from the other characters, who are themselves barely developed. Her evident crush on Van Damm is the most convincing sign of emotional connection. (It’s wearyingly spun into grand mutual respect – the kind where oldsters ceremoniously ask each other for one last dance and do so to fadeout.)

But she has her tragic side, you see – a son who died in the Great War, which the film signposts early on, ready for a lugubrious long-term wind-up. So when officials close the theater for fear of crowds gathering outside during the Blitz, it’s no surprise to hear her invoke his memory on a soapbox.

And what an elegy it is. The poor boy, you see, never saw a flesh-and-blood naked lady before he died, but only horrid “French postcards” (which, if one can imagine anything more mortifying, she found under the hero’s mattress). Would that no soldier suffer so ever again!

It’s that oldest call to arms: Take it off, ladies, and think of England.