The U.K. vote sent the pound plunging to a 31-year low last month and fueled a rally in the yen, which is sought by investors during times of market turbulence. Dollar fluctuations and currency volatility have posed a "nightmare" for companies, dragging down earnings for 357 North American firms in the fourth quarter, according to FiREapps. That was the most companies under duress since at least 2011.

Currency swings can undermine the competitive pricing of companies seeking to sell their products in foreign countries. Firms also take a hit when they account for revenue denominated in weaker overseas currencies, unless they hedged their exposure.

Many U.K. businesses have put investment plans on hold amid uncertainty about the U.K.'s future relationship with the EU and other trading partners. For some companies, the main areas of concern are whether they will retain access to low-cost labor from other EU countries as well as the EU common market. Other firms aren't sure whether they'll face tariffs or onerous conditions to sell their goods in export markets.

One example is Burberry Group Plc, which reported an increase in U.K. sales in the final weeks of June as visitors flocked to its domestic stores to take advantage of the weak pound. But Chairman John Peace said that the company was pausing plans for a plant investment in Leeds, England, because of uncertainty about Brexit. Burberry said the project will go ahead, but its timetable may be affected.

Koester said many companies hadn't sufficiently hedged their currency exposure in the run-up to the U.K. vote, while others weren't able to quantify the extent of their foreign-exchange risk even a week after the poll concluded.

"You're seeing people getting caught by surprise, thinking that these volatile times would soon be over—and they're kidding themselves," Koester said.

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