The cause of death was given as compression to the neck, Scotland Yard said.
Glushkov, a longtime associate of the oligarch, had worked for various Berezovsky enterprises including the auto factory AvtoVAZ and flagship Russian airline Aeroflot.
The death came a week after former Russian spy Sergei Skripal and his daughter Yulia were left critically ill from a nerve agent poisoning in the city of Salisbury.
The Russian embassy has said it sought Glushkov's extradition in 2015, but the British government refused, Sky News reported.
Police said a post-mortem showed no sign of a violent struggle, and an inquest recorded an open verdict after hearing conflicting evidence.
British counterterrorism officers are leading the investigation "as a precaution" because of Glushkov's associations.
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Mr Berezovsky was found hanged in the bathroom of his Berkshire home in 2013.
One of Mr Glushkov's neighbours, Patricia Egan, said police had questioned local residents about what they had seen and heard of the businessman or his dog.
He was arrested in 1999 and put on trial for allegedly embezzling $7m (£5m) from Aeroflot, and sentenced in 2004 to three years, three months in prison.
Nikolai Glushkov, 69, was found dead at his house in southwest London at about 10:46 p.m. on Monday.
Detectives were keeping an open mind, police said, and appealed for any information that would assist the investigation. "It is unacceptable and we consider this situation as a failure of the UK's global liabilities under the Vienna convention of consular access", he said, adding that a relevant inquiry had been sent to the British authorities immediately after the news about businessman's death at the beginning of the week.
A murder investigation was launched Friday into yet another suspicious incident involving yet another Russian exile living in Britain - the latest episode coming just over a week after a former Kremlin spy and his daughter were poisoned.
Glushkov was granted asylum in the United Kingdom in 2010.