There is an indelible moment in “Airplane!” (1980), a film directed by Jim Abrahams, David Zucker, and Jerry Zucker, that could serve as a comedic litmus test: When a flight from Los Angeles to Chicago encounters a set of problems, not least the loss of the cockpit crew, a passenger is enlisted to take the helm, a war veteran with a fear of flying. When asked by a doctor on board if he can land and fly the plane, the potential pilot answers: “Surely, you can’t be serious.” To which the medical professional, with the straightest of faces, responds: “I am serious. And don’t call me ‘Shirley’.”

Should that joke prompt even the slightest amusement, Jim O’Hanlon’s “Fackham Hall” will likely tickle your funny bone. There are any number of variations on misapplied grammatical logic in a script written by two sets of brothers, Steve and Andrew Dawson along with Jimmy and Patrick Carr, with the help of Tim Inman, presumably an only child. Fans of stand-up comedy will be familiar with Jimmy, a consummate crafter of jokes, some of them very rude indeed.

Mr. Carr has a supporting role playing a vicar inadvertently given to making salacious comments from the pulpit, and he’s very funny here. The screenplay he had a hand in writing has a panoply of gags strewn about the proceedings, all of which are clever but only some of which land. But, then, that’s the nature of the beast, innit? “Fackham Hall” is in the catch-as-catch-can spirit of spoofs like “Airplane!,” Mel Brooks’ “Blazing Saddles” (1974), and Monty Python’s Flying Circus, albeit less the troupe’s movies than the television series that preceded them.

Parody of this sort requires a sitting target, and “Fackham Hall” has two of them, the primary being the popular British period drama, “Downton Abbey.” The other is a locked-room mystery, a species of detective fiction popularized by Agatha Christie and currently exemplified by the recent “Knives Out” film series.

More so than some of its predecessors, Mr. O’Hanlon’s picture is effective at tweaking the cinematic conventions of the source material. The director of photography, Philipp Blaubach, suffuses the proceedings with a softly stated range of bland tones redolent of any number of programs seen on “Masterpiece Theater.” The soundtrack by David Arnold and Oli Julian, is, in equal measures, august and flippant. The production design by Chris Richmond and Andy Holden-Stokes is more straightforward, notwithstanding a stray trap door or salacious bit of signage.

As befits comedy that trades in groan-worthy puns and by-the-book apercus, the cast plays it straight. Damien Lewis channels Stan Laurel as the befuddled patriarch of Fackham Hall, Lord Davenport, and the cast has a field day with all the requisite tut-tutting and stiff upper-lipping. The shtick here is dry in affect and, as such, endearing, though Sue Johnston’s foul-mouthed turn as Great Aunt Bonaparte is a fairly tired canard. Most of “Fackham Hall” is tried-and-true — we even get a variation on Abbott and Costello’s “Who’s On First” routine. One is hard put to say whether the overall tone is an homage to precedent or indicative of a lack of imaginative grasp.

The plot, in as much as it matters, concerns the excesses of the idle rich, a love affair that upends cultural propriety, and a murder that sets a family into chaos. Will viewers who made “Downton Abbey” a pop culture phenomenon take up the gambit offered by Messrs. O’Hanlon, Carr and crew? British audiences may relish the umpteenth takedown of cultural archetypes; American viewers, the blatant dum-dum humor. Those of us who came of age taking pleasure in the misadventures of Bertram Wilberforce Wooster or the athletic achievements of the Upper Class Twit of the Year will take heart that some things never change, and then plunk down our farthings.