The Russian government has ordered the British Council to close down its two offices outside Moscow by the beginning of January.
President Putin has acted against the activities of foreign NGOs
The Russian foreign ministry said the council, which promotes British culture abroad, was operating illegally.
The British PM's office denied that the Council had acted illegally.
Russian officials have said the move was a retaliatory measure in the ongoing dispute over the London murder of Russian exile Alexander Litvinenko.
Relations between the UK and Russia have worsened since the former KGB agent was murdered in November 2006.
In July, Britain expelled four Russian diplomats over Moscow's refusal to extradite a key suspect in the murder.
Russia followed by expelling four British diplomats.
Russian foreign ministry officials said the British Council had violated Russian laws, including tax regulations.
The Russian Foreign Minister linked the move to the Litvinenko case
But in an interview with the BBC, Foreign Minister Sergei Lavrov explicitly linked the order to Britain's expulsion of Russian diplomats in July.
He said Russia had been left with no choice but to retaliate over the affair.
Both the British Council and the UK Foreign Office said the council was fully compliant with Russian tax laws and operates on the basis of an agreement signed in the 1990s.
The council announced three months ago that it was closing nine regional offices by the end of the year and transferring operations to Russian partners.
Those closures leave the headquarters in Moscow, plus offices in St Petersburg and Yekaterinburg.
But a spokesman for UK Prime Minister Gordon Brown rejected the Russian allegations. "The British Council's activities in Russia are compliant with Russian and international law under the Vienna Convention and the 1994 cultural agreement between Britain and Russia," he said.
"The Council is fully entitled to operate in Russia, both in Moscow and elsewhere. We, the Council and its Russian partner organisations have every intention that its programme will continue," the spokesman said.
A British Council spokeswoman told the BBC that the council intends to continue its operations in Russia at the three remaining offices.
The council is a registered charity funded by the British government. Its stated purpose is to promote British culture and education and build relationships between people in the UK and other countries.
Moscow has acted to curb NGOs in recent years, accusing foreign governments of using them for political purposes.