In the story, Kermit the Frog, Fozzie Bear, and Gonzo the Great play newspaper reporters for the Daily Chronicle. Kermit and Fozzie, specifically, are playing identical twin reporters, which becomes the source of a running gag - supposedly, nobody can tell they are twins unless Fozzie wears his hat. The two are eventually assigned to investigate the theft of valuable jewels from fashion designer Lady Holliday (Diana Rigg), which they have to beg for after their boss fires them following the Daily Chronicle's headline about the two of them joining the staff (while the other papers report on the jewel heist). They travel to London to interview her, but with only $12 for the trip, they're forced to fly in the airplane's baggage hold and are thrown out of the plane as they arrive over Britain. They stay at the dilapidated (but free) Happiness Hotel, run and populated by Pops, Scooter, Rowlf, and Dr. Teeth and The Electric Mayhem. When Kermit seeks out Lady Holliday in her office, however, he instead finds his love life Miss Piggy and fails to recognise her, mistaking her for the fashion designer. Piggy masquerades as Lady Holliday, even going so far as to sneak into a ritzy townhouse (located at 17 Highbrow Street) in order to impress Kermit with her dwellings, much to the surprise of the true British residents (one of whom is John Cleese).
At a night club restaurant, Lady Holiday's necklace is stolen by her jealous brother Nicky (Charles Grodin), assisted by Carla, Marla and Darla, three of her put-upon fashion models. Despite Nicky's instant attraction to Miss Piggy, they successfully frame her for the theft and proceed to steal an even more valuable prize--the coveted Baseball Diamond, which is on display at a local gallery, the Mallory Gallery. Kermit's crew, along with their friends from the Happiness Hotel, have no choice but to intercept and catch the thieves themselves in order to clear Miss Piggy's good name. Piggy, meanwhile, has escaped from prison and, in a bout of serendipity, finds a motorcycle which she uses to literally crash into the film's climax, knocking Nicky, who is holding Kermit hostage, out in the process. Carla, Marla and Darla confront Piggy, only to be quickly dispatched by a flurry of furious karate chops. The Muppets then return to America the same way they departed, being thrown out of the cargo hold and parachuting back to Earth, over the end credits.