"I was relieved to find out the prime minister stood firm and explained to Mr Medvedev that there can be no compromise on that."
She added: "Britain once again has shown that it would not short-change its principles in the face of bullying and blackmail."
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 co-operate saying it would be against its constitution to do so.
On the Litvinenko case a senior security official told Newsnight there were "very strong indications it was a state action."
The BBC has been told 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."
Russia maintains there is no evidence its intelligence service were responsible for the death.
In a statement, the Russian Prosecutor General's Office, which has also been probing the case, said: "The investigation has made significant progress and does not possess information that any intelligence service was involved in the crime."
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