Counter-terror police are investigating the death of the 68-year-old tycoon, whose body was found at his home in New Malden, southwest London, on Monday.
A Russian exile in London has told Sky News he has been spoken to by police about his own safety in the wake of Mr Glushkov’s death.
Sky’s defence correspondent Alistair Bunkall said he understands measures are now under way to protect some Russian exiles from harm on British soil.
A Metropolitan Police spokesman said the force had given “security advice to individuals” but refused to comment on whether they were Russians.
A post-mortem found the cause of Mr Glushkov’s death was compression to the neck, prompting police to launch a murder investigation.
He was found hanged, perhaps to make it look like suicide, Sky sources have confirmed.
His death came days after the attempted poisoning of former spy Sergei Skripal and his daughter Yulia in Salisbury, but police have not linked the two incidents.
Mr Glushkov, a prominent critic of the Kremlin, had received political asylum in Britain after being jailed in Russia for money laundering and fraud.
Scotland Yard said its counter-terrorism command is leading the investigation “because of the associations Mr Glushkov is believed to have had”.
Russia’s Investigative Committee, which reports directly to President Vladimir Putin, has also opened a murder investigation into Mr Glushkov’s death.
The Russian embassy said it had sought Mr Glushkov’s extradition in 2015 “for committing a number of severe financial offences on the territory of Russia”, but the British government refused.
One of Mr Glushkov’s friends was late Russian oligarch Boris Berezovsky, who fled to London in 2000 following a row with Mr Putin.
After Mr Berezovsky was found hanged in the bathroom of his Berkshire home in March 2013, Mr Glushkov told The Guardian he would “never believe” his friend took his own life.
An inquest into Mr Berezovsky’s death recorded an open verdict.
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Mr Berezovsky was also a friend of Russian dissident Alexander Litvinenko, who was poisoned with radioactive polonium-210 in London in 2006.
Police and MI5 are expected to examine allegations that a series of deaths on UK soil, including the Berezovsky case, may be linked to Russia.