“It has been a nightmare,” Ms. Danesh said. After the coup, everything from Dropbox to PayPal ceased to function efficiently. There were delivery delays. “The factory kept telling me that everything was fine on the phone, but I could tell it was not,” she said. By this time, she had signed deals to sell her stock at Harvey Nichols in London and to boutiques Dubai and the Spanish island of Ibiza.

Many pieces in Ms. Danesh’s initial 2017 summer collection were so delayed they had to be released as part of her subsequent cruise collection. “I still use the Istanbul factory because of the product quality,” she said. “But I have moved shipping to Britain, which eats into margins but has also reduced the risk that I don’t deliver orders in time.”

Despite the troubles, some fledgling brands with design studios in Istanbul remain upbeat. Manu Atelier is a small, family-run accessories label housed in an 18th-century building on a cobbled street in the Beyoglu district, an ancient quarter known for its leatherwork trade. Founded in 2014 by Merve and Beste Manastir, daughters of a leather craftsman who personally signs off on every piece, the company has grown rapidly in the last three years thanks to savvy use of social media, competitive prices and glowing endorsements by Vogue and Eva Chen of Instagram. The label is stocked at Selfridges and Saks and now has an office staff of 16 and a workshop of 30 artisans.

“It has been a chaotic time,” Merve Manastir said. “Locally, people have been less keen to go out and spend money, and visitor numbers are down. But honestly, we don’t think about borders that much. Our business has grown so much internationally that we are less exposed in our home market.