The last time Christiani Pitts starred on Broadway, in 2018’s wildly misbegotten “King Kong,” she played second fiddle to an animatronic ape. For roughly the first half hour of “Two Strangers (Carry a Cake Across New York),” the new, London-based musical that brings this brightly appealing actress and singer back to the stage, it seems as if fate may have dealt her another turkey.

“Two Strangers,” a two-character piece that earned rave reviews across the pond — never a guarantee that a production will be bearable, let alone worth the ticket price — casts Ms. Pitts as Robin, a Brooklyn-bred woman in her 20s working in a Manhattan coffee shop. Robin’s only slightly older sister is about to marry a much older and very wealthy Englishman, and she sends her sibling to greet the man’s son, Dougal, who has flown in for the wedding.

After they meet-cute at the airport — Soutra Gilmour’s revolving set evokes a baggage claim site, then cleverly uses the items representing luggage to lay out a variety of settings — Robin reluctantly agrees to let Dougal, who is as wide-eyed and eager as she is seemingly closed-off and sarcastic, to accompany her as she picks up that cake, one of numerous other chores her sister has assigned her.

It soon becomes clear that neither Robin nor Dougal are really wanted at the wedding, and for a while, “Two Strangers” threatens to become a sappy account of two opposites drawn together by their sad-sack circumstances. Yet somewhere in Act One, the show — the first crafted by Jim Barne and Kit Buchan, who collaborated on the book, music, and lyrics — begins to pick up steam, and those stories and the characters themselves grow a little less predictable, and a bit more compelling.

There are sober moments along the way, which reminded me, at least tonally, of “The Last Five Years,” Jason Robert Brown’s dour chamber musical, inspired by the dissolution of his first marriage. Yet Robin and Dougal are livelier and more endearing than the selfish writer and enabling girlfriend/wife in Mr. Brown’s show, and Messrs. Barne and Buchanan’s eclectic, pop-based score provides both quirky duets and solo numbers, including a couple of fetching ballads, to flesh them out. 

The English actor, Sam Tutty, who introduced Dougal in the U.K., delivers the boyish energy and vulnerability the part requires. An Olivier Award winner for his performance in the title role of the West End production of “Dear Evan Hansen,” Mr. Tutty also brings considerable lung power, belting the more muscular numbers to the back row, and he can play the clown adroitly given the right material — like a merry romp called “American Express,” which finds Dougal and Robin painting the town on someone else’s dime.

Yet it’s Ms. Pitts’s more nuanced performance that gives this musical rom-com, nimbly directed and choreographed by Tim Jackson, more emotional punch than you might expect, at least at its high points. One ballad, “He Doesn’t Exist,” in which Robin tries to comfort and warn Dougal about his absent father, is an especially lovely showcase not only for her robust singing, but for an open-hearted expressivity that can be as tender as her comedic instincts are sharp.

If “Two Strangers (Carry a Cake Across New York)” is more engaging than its premise, or that unwieldy title, would suggest, this leading lady deserves a lot of the credit — and I hope I don’t have to wait another seven years to see her on Broadway again.