Alexander Perepilichnyy, a businessman who had sought refuge in Britain three years ago after falling out with organised criminals, collapsed outside his mansion near Weybridge earlier this month.
The 44-year-old had apparently been in good health. Surrey Police said a post mortem examination has proved "inconclusive" and that further tests had been carried out to try to establish a cause of death.
He was discovered when officers were called to his home on a luxury private estate shared with seven multi-million pound properties shortly after 5pm on a Saturday two weeks ago, and declared dead half an hour later.
Suggestions that he had been out running were not confirmed by Surrey Police.
Police said they had been made aware of Mr Perepilichnyy's link to the Swiss investigation and it "forms part of the inquiry". The death was being treated as "unexplained".
Mr Perepilichnyy was a key witness against a network of corrupt Russian officials and crime figures known as the "Kluyev Group", according to a newspaper.
The network is said to be implicated in a series of multi-million pound tax frauds as well as the death in custody of Sergei Magnitsky, a whistle-blowing Moscow lawyer, The Independent reported.
It said that Mr Perepilichnyy was the fourth person to be linked to the scandal who had died suddenly.
His evidence was said to have revealed how Moscow tax officials had allegedly enriched themselves following a tax fraud against a British investment fund.
They were said to have used Swiss-based bank accounts to buy luxury property in Dubai and Montenegro.
Swiss prosecutors has opened an investigation earlier this year into a number of accounts at Credit Suisse after Hermitage Capital Management passed them a file of evidence that was said to implicate the Russian officials.
A source with knowledge of the investigation told The Independent: "Perepilichnyy was the guy who brought all the evidence they needed to open the investigation.
"He brought with him records of shell companies, Credit Suisse accounts, property transactions. The whole lot."
Hermitage Capital had been one of the largest foreign investors in Russia until it fell victim to a complex £144 million tax fraud scheme involving tax officials and others from the Ministry of Interior.
The firm hired Sergei Magnitsky, a Moscow lawyer, to investigate. Mr Magnitsky testified against the police and was later charged by the same officers of tax evasion.
He was jailed for a year and died in prison after being refused medical attention and beaten instead. The Kremlin's own human rights council found that his death was the result of "calculated, deliberate and inhumane neglect".
The death of Mr Magnitsky, and Hermitage's efforts to have those responsible brought to justice, have resulted in major diplomatic tensions with Russia. The US has barred 60 individuals linked to Mr Magnitsky's death from entering the country.
The Swiss Attorney General confirmed that Mr Perepilichnyy had given evidence to a federal prosecutor.
Surrey Police said the investigation into Mr Perepilichnyy's death had been passed to the coroner ahead of an inquest.
A spokeswoman said: "Surrey Police continues to treat the death of a man in his 40s who collapsed in Weybridge on Saturday November 10 as unexplained.
"The death remains unexplained while we await results of the post mortem and toxicology tests, and we are working closely with the coroner's officer while the investigation remains ongoing.
"The incident took place in Granville Road shortly after 5.15pm and we received a report that a man had collapsed in the road."
Ambulance staff attended the scene but the man was pronounced dead around 25 minutes later, the spokeswoman said.