LONDON—Nikolai Glushkov, a Russian émigré, lived alone in a weather-beaten row house in South London with an aging dog and a cat named Braveheart. It was the waning days of March, and he was readying himself for something big.

The onetime finance director of Russia’s flagship airline, he was preparing for a trial in a London court. He told friends it would prove his innocence of longstanding financial charges by Russian authorities and expose Aeroflot Russian Airlines as a front for Russian security services. The case could...