LONDON — Who’d have thought an enormous mound of fur would be the most endearing sight on the London stage? I’m referring to the outsize woodland creature of the title in “My Neighbour Totoro,” who is eliciting gasps of surprise and delight at the Barbican Theater through Jan. 21.

Making an entrance well into the first act, this piece of larger-than-life fluff — a puppet controlled from within by people we don’t see — brings an immediate sense of excitement to this adaptation of the beloved 1988 animated film of the same name, a banner work from Studio Ghibli of Japan. Reworked for the stage by Tom Morton-Smith, it has arrived as a Royal Shakespeare Company production; the play’s composer, Joe Hisaishi, gets an executive producer credit.

The movie, directed by Hayao Miyazaki, overcame some sniffy early reviews and is now regarded as a classic for the studio, whose subsequent “Spirited Away” won the Oscar for animation in 2003. (A theatrical “Spirited Away” opened earlier this year in Japan.)

The challenge with “My Neighbour Totoro” was to amplify a sweet but slender movie running less than 90 minutes whose enchanting visuals could seem a stretch for the stage. In fact, as directed by Phelim McDermott, who divides his career between theater and opera, this tale of two sisters displaced to rural Japan in the 1950s exerts its own distinct magic.

You share the characters’ sense of expectation as 10-year-old Satsuki and her 4-year-old sister, Mei, adjust to their new home in the countryside. Their father has moved the family from Tokyo to be nearer to the girls’ mother, who is hospitalized with an unspecified but serious illness.

The siblings’ imaginations soon run riot as they discover any number of creatures — including “soot sprites” resembling dancing particles of dust — that the adults around them can’t see. The show’s visual invention honors the animal kingdom, and the puppeteer Basil Twist and his hardworking team spring one enchantment after another on the audience. (The puppets are the glorious handiwork of Jim Henson’s Creature Shop.) The emphasis throughout is on the characters’ surroundings befitting Miyazaki, a lifelong environmentalist: The woods are sites of enchantment and discovery, not places marked out by dread or fear, and Tom Pye’s flexible set shifts locations with ease.

Any potential cutesiness is kept at bay. Ami Okumura Jones and Mei Mac, both adults, play the girls with a zestful appetite for experience that never turns cloying, and Dai Tabuchi is infinitely touching as their kindly father.

You could argue that the ending feels rushed and unconvincing, as if the creators were overeager to deny the threat of mortality that takes center stage as the health of the girls’ mother (Haruka Abe) worsens. The darkening of the narrative then does an abrupt about-face in time for a pat feel-good finish that is the play’s only misstep. But by that point, the audience has long since given itself over to the giddy parade of puppets, from some sweetly entrancing butterflies that seem to dance in the air to the gleaming Catbus, an automotive creature that, after Totoro, is probably the best-remembered character of the film.

The Royal Shakespeare Company hasn’t produced a show of such commercial potential since the musical “Matilda” over a decade ago — coming to Netflix in a film adaptation this holiday season. Like “Matilda,” “My Neighbour Totoro” is family entertainment that adults might like even more than children.

The kindness, empathy and generosity of spirit that “My Neighbour Totoro” evokes are infectious. But it’s the capacity for evil that drives a West End revival of “Good,” a 1982 play by C.P. Taylor. (That Scottish playwright died the year before the play’s premiere by, yes, the Royal Shakespeare Company.) The current production, from the director Dominic Cooke, runs at the Harold Pinter Theater through Dec. 24.

The protagonist is a mild-seeming German academic, John Halder (David Tennant), whom we first encounter in Frankfurt, in 1933. Antisemitism is rising in Germany, but Halder seems more preoccupied with domestic issues. Early on, he reassures his close friend Maurice (Elliot Levey), a Jewish psychiatrist, that any worries about the gathering climate of fear can be put to one side: Targeting Jews, he says, “is not practical,” given their importance to Germany’s economy and society, so there’s little cause for alarm. In any case, Halder is too busy navigating an extramarital affair and a mother with dementia to pay much heed to history’s horrific onward march.

The author’s cunning across two brisk hours is to chart an apparently decent man’s decline into moral depravity: What begins as casual indifference ends up as active participation. The sight of Halder, in full SS uniform, standing at the ready at Auschwitz is followed by a climactic visual coup de théâtre that comes as a genuine shock.

The production is forbiddingly spare and unfolds on a minimal monochrome set, from Vicki Mortimer, that eerily evokes a mausoleum. Tom Gibbons’s invaluable sound design brings out the full horror of Kristallnacht, with shattering windows, heard but not seen, contrasting with the clinking glasses we heard earlier in the show, at a time when civility seemed possible.

Cooke, the director, has pared the cast back to three actors, with Levey and the female lead, Sharon Small, deftly playing multiple roles. The decision to conjoin some parts heightens an awareness of Halder’s tenuous purchase on reality, as if his wayward thoughts were tumbling from his mother to his wife to his lover, with Small taking all those parts and a further, altogether different one as well.

This “Good” wouldn’t be anywhere near as good as it is without Tennant, a TV name (“Doctor Who”) and stage regular whose likability puts you in Halder’s corner at the start. Speaking in his natural Scottish accent, Tennant initially gives off the air of a genial bookworm with whom you might discuss Goethe over a drink. But by the time he is staring the audience down in full Nazi regalia, you’re reeling from a portrait of psychosis whose shivery power is hard to shake.

My Neighbour Totoro. Directed by Phelim McDermott. Barbican Theater, through Jan. 21.
Good. Directed by Dominic Cooke. Harold Pinter Theater, through Dec. 24.