Berezovsky had helped Russian President Vladimir Putin rise to power before becoming a vocal critic of Putin.
Police said the death was being treated as unexplained, adding that the counterterrorism team would lead the investigation "as a precaution because of associations that the man is believed to have had".
Nikolai Glushkov, 69, a former deputy director of Aeroflot who had twice faced fraud charges in his native Russian Federation, was found dead at his home in New Malden, south west London, late on Monday night. It did not identify him by name.
Glushkov, who was 68 when he died on Tuesday, rose to wealth in the 1990s as a lieutenant of Berezovsky, the oligarch who amassed vast wealth and influence under the Boris Yeltsin's government but fled to Britain after falling out with Vladimir Putin. An inquest failed to establish if he had committed suicide or died from foul play.
Glushkov worked in the 1990s for the state airline Aeroflot and Berezovsky's LogoVAZ vehicle company, according to media reports. He spent five years in jail and was freed in 2004.
Britain granted Berezovsky political asylum three years later on the grounds his life would be in danger if he went back home.
It came as Berezovsky fell out with Putin and fled to Britain.
EU, Japan start push for exemptions from Trump tariffs
Trump tweeted on Friday that he spoke with Australian Prime Minister Malcolm Turnbull about trade and military cooperation. However, he said "real friends" of the U.S. could win waivers from the measures, which come into force after 15 days.
He noted that a large number of Russian exiles including Berezovsky, and Berezovsky's close friend Alexander Litvinenko, had died under mysterious circumstances.
Prime Minister Theresa May has said it is "highly likely" that Russian Federation was behind the attack, which used the nerve agent Novichok and has left Skripal and his daughter fighting for their lives.
Glushkov is believed to have two grown up children, Natasha and Dima, and an ex-wife who lives in Moscow.
But his case was revived by a Moscow court last year, which sentenced him in absentia to eight years for allegedly embezzling more than $122m from Aeroflot. They were found unconscious on a bench in Salisbury.
May gave Russian Federation until the end of Tuesday to respond to her allegations.
He told reporters on Tuesday that London wants "Russia to declare these programs now". If they do not respond, she said, the United Kingdom.