LONDON — Big-name American shows are finding their customary perch here, but so are lesser-known plays and playwrights, for whom the city is increasingly hospitable. More than ever, it’s possible for Londoners to get a comprehensive view of the theater in the United States without being there.

Two major musical theater prizewinners have opened here recently: “The King and I” and “Fun Home,” which scooped up nine trophies between them at the 2015 Tony Awards and have crossed the Atlantic to splendid results, both critically and financially. “Fun Home” opened on June 27 to near-ecstatic reviews and is selling briskly at the adventurous Young Vic playhouse, well away from the commercial West End.

Meanwhile, the producers of “The King and I” took the unusual step of announcing that their production had broken the box-office record for its first week at the capacious London Palladium, grossing around $1.4 million. (London theater folk are usually tight-lipped about box-office receipts, and grosses here generally go unreported.)

In a town whose lineup of musicals increasingly replicates that on Broadway, it shouldn’t surprise when prizewinners hop the pond. “The Book of Mormon” and “Hamilton” — two big hits here, as in New York — are built to travel, and do.