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Mr Litvinenko had been investigating the murder of Russian journalist Anna Politkovskaya, a harsh critic of Mr Putin and Russian policy in Chechnya, who was killed in Moscow last month.
"It is tasteless, colourless, odourless. It takes about a gram - you know, a large pinch of salt like in your food - to kill you."
Russian tycoon Boris Berezovsky, who also lives in Britain, said thallium was a "special" poison, that "you couldn't just get over the counter".
"You could say it is only available to secret services," he said.
There has been no comment from the Kremlin and the Russian media is reportedly keeping quiet on the incident.
In a book, Blowing up Russia: Terror from Within, Mr Litvinenko alleged that agents from KGB successor FSB co-ordinated the 1999 apartment block bombings in Russia that killed more than 300 people.
Russian officials blamed the explosions on Chechen separatists and in that year the Kremlin launched a new military offensive on Chechnya.
Mr Litvinenko's friend Alex Goldfarb, who has been visiting him in hospital, said doctors told him he had a 50/50 chance of surviving the next three or four weeks.