When Efe Cakarel picked London as a new base for his video streaming company, he was counting on its location, capital markets and infrastructure, but also on the city's reputation as a hub for talented people from Europe and beyond.

Four years later, the 38-year-old entrepreneur has a half-dozen engineering vacancies that he says haven't been filled for nearly a year because of a local shortage of top-tier programmers. Immigration restrictions, he says, have made it harder to tap into the global pool of talent, costing his 7-year-old start-up, MUBI, subscribers and revenue.

"We're ready to grow, but without the right workers, we just can't expand," he said.