Berezovsky was found deadin March 2013 at his ex-wife's home in Berkshire.
Nikolai Glushkov, 68, was discovered dead late on Monday at an address in Clarence Avenue in suburban south-west London.
He added: "too many deaths [of Russian emigres] have been happening". He was sentenced to eight years in prison by a Russian court for the theft of millions of dollars from Aeroflot when he served as its director in 2017.
The White House on Monday condemned the poisoning of the ex-Russian spy in the U.K."The use of a highly lethal nerve agent on U.K. soil is an outrage".
They were found in Salisbury, around two and a half hours from London.
Relations between Britain and Russian Federation have been strained since the murder in London of former KGB agent Alexander Litvinenko, who died in 2006 after drinking green tea laced with radioactive polonium-210.
Ms Rudd said the Government takes seriously allegations that the deaths, dating back to 2006, may have some links to Russian Federation.