Britain’s top diplomat on Friday accused Russian President Vladimir Putin of ordering a nerve-agent attack that left an ex-double agent and his daughter fighting for their lives, as police launched a murder investigation into the death of another Russian exile in the U.K.

Police said an autopsy showed businessman Nikolai Glushkov, a 68-year-old Kremlin critic and former top executive of Russian state airline Aeroflot, was found dead from “compression to the neck” at his home March 12, about a week after the poisoning on British...