It’s not just the distilleries’ small size that foreign consumers find attractive. While selling something like American gin in London might seem like bringing liquefied coals to Newcastle, there are important differences between the products of industrial-scale distilling and these new entrants — between, say, gins from the big traditional brands like Beefeater and Tanqueray and those from the likes of Ransom.

All gin starts off by fermenting a soupy mash of yeast, water and grain — though anything with a lot of organic sugars, like potatoes or sugar beets, will do — and then distilling it to get a high concentration of alcohol. During distillation, the alcohol is steeped in a basket of “botanicals” — mostly juniper, along with other spices like anise and coriander and citrus elements like lemon peels — to give it its flavor.

Though every distiller uses a different mix of botanicals, over time the big brands have gravitated toward a narrow set of pepper and floral notes. American craft gins, by contrast, are all over the flavor map. Some, like Corsair, out of Nashville, are heavy on oranges and lemons; others, like Old Tom from Ransom, are aged in barrels to provide a woody, vanilla overtone.

This broader palette of flavors is particularly appealing to a younger generation of innovative bartenders in global crossroad cities like London, Paris and Berlin, who not only cater to an educated, international clientele but are increasingly international themselves, sharing new recipes with colleagues online and traveling to conferences and competitions in other countries.

“There’s a lot of demand among the new high-end cocktail bars,” Ms. Le Prestre said. Many of the best bartenders, she said, “have been to the United States and tasted U.S. products, and they come back here looking for these.”

And in an increasingly competitive cocktail market like London, having the latest American craft spirit — whether it’s bourbon, rye or gin — is a must.

“It’s like giving them a new tool in their arsenal,” Mr. Vachon said. “Customers can go in and expect 10 different gins. Now your bar stands out. You are offering a different experience to customers.”