Newsnight's Mark Urban investigates the claims
The murder of former Russian agent Alexander Litvinenko was carried out with the backing of the Russian state, Whitehall sources have told the BBC.
A senior security official told Newsnight there were "very strong indications it was a state action".
Mr Litvinenko, who was a fierce critic of former Russian President Vladimir Putin, was poisoned in London in 2006.
UK investigators suspect former KGB agent Andrei Lugovoi of the murder, but he has always denied any involvement.
The BBC has been told that Russia's internal security organisation, the FSB, operated under Mr Putin with far more autonomy than the organisations usually entrusted with foreign espionage operations.
Our source said: "We very strongly believe the Litvinenko case to have had some state involvement."
Newsnight has also learned that officers at MI5 believe they thwarted an attempt last summer to kill another Russian dissident, Boris Berezovsky.
Mr Litvinenko died after drinking tea laced with polonium 210
The BBC's source said the Berezovsky incident showed "continued FSB willingness to consider operations against people in the West".
And they claimed the targeting of Russian government critics in the UK had serious diplomatic repercussions, saying: "[It] messes up the relationship big time."
In November, head of MI5 Jonathan Evans expressed concern that there had been "no decrease" in the number of Russian covert intelligence officers operating in the UK since the end of the Cold War.
The service believes there are around 30 operating from Russian diplomatic missions here.
In May 2007, the Crown Prosecution Service formally submitted an extradition request to Moscow for Mr Lugovoi to stand trial in Britain.
That request remains current, but Russia has refused to cooperate saying it would be against its constitution to do so.
UK Prime Minister Gordon Brown is thought to have raised the case as he held his first face-to-face talks with new Russian president Dmitry Medvedev at the G8 summit in Japan.