British counter-terrorism police said it was investigating the death "because of the associations Mr. Glushkov is believed to have had".
He was friends with the late oligarch Boris Berezovsky, who famously fell out with Putin.
Russia's Investigative Committee has launched a criminal case over Glushkov's death of Nikolai Glushkov.
Glushkov was found dead at his south London home on Monday (Tuesday NZT).
United Kingdom police said there was at this stage no evidence linking the death of Mr Glushkov to the attempted murder of the former spy Sergei Skripal, 66, and his daughter Yulia, 33, in Salisbury, police say.
Both Britain and Russian Federation have launched their own investigations into the poisoning, which has led to an ongoing diplomatic crisis. The two are in a serious condition in hospital. Putin's spokesman has denounced the comment as "shocking and inexcusable".
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His family feared he might have been murdered by enemies in Russian Federation, but British police and forensic experts concluded that Berezovsky had committed suicide.
In light of the Salisbury attack, British police are looking again at the deaths of more than a dozen Russians in Britain, including Berezovsky.
At the time, Mr Glushkov said he believed his friend had been murdered, telling The Guardian: "I don't believe Boris died of natural causes".
"Mr Glushkov, a retired financial director, was a Russian national who had lived at that address for two years".
He is accused of organizing a large-scale fraud scheme, embezzling $7 million from a Russian airline.
Britain granted Berezovsky political asylum three years later on the grounds that his life would be in danger if he went back home. In March 2017, Moscow's Savelovsky District Court handed him a second eight-year sentence in absentia for the embezzlement of Aeroflot's funds.
Last year, Glushkov appeared on a list published by the Russian Embassy in London of Russian citizens wanted for serious crimes whom the United Kingdom had refused to extradite.