Russian security officials say they have arrested and charged two brothers with links to British interests.
TNK-BP is the UK's largest joint venture in Russia
Ilya Zaslavsky is a manager at the TNK-BP oil joint venture, his brother Alexander is the head of the British Council's Moscow Alumni club.
The two, who have joint US and Russian citizenship, were gathering classified data for foreign firms, the FSB said.
The arrests are the latest in a series of incidents which has caused serious frictions between Russia and the UK.
British Council work was curtailed last year in a row over the death of ex-security agent Alexander Litvinenko.
The Moscow offices of the British oil giant were raided by the authorities on Wednesday.
Nov 2006: Alexander Litvinenko dies in London
May 2007: UK accuses ex-KGB agent Andrei Lugovoi of murder
July: Russia refuses British request to extradite Mr Lugovoi
July: UK expels four Russian diplomats
July: Russia expels four British embassy staff
Dec: Russia orders British Council to shut two offices
Jan 2008: British Council re-opens both offices
17 Jan: Both offices suspend work
Russia's security agency, the FSB, has confirmed that the raids were related to the Zaslavsky case.
"During the raid, material proof confirming the industrial espionage was found and confiscated," it said in a statement.
This included business cards of foreign military agencies and the CIA, it said.
But analysts say the objective of the authorities is much broader than prosecuting a case of industrial espionage, as they attempt to re-assert control over an oil industry, much of which was sold off to foreign investors in the 1990s.
The BBC's Rupert Wingfield-Hayes in Moscow says TNK-BP, which is the UK's largest joint venture in Russia and Russia's third-largest oil company, is the last in the industry still beyond the Kremlin's control, but perhaps for not much longer.
Last year state gas giant Gazprom bought a majority stake in the vast Kovykta field from TNK-BP, and is rumoured to be now seeking to buy a stake in the joint venture itself.
The row is the latest development in ongoing tensions between London and Moscow that began with the murder of Mr Litvinenko, a former KGB agent, in London in November 2006.
The UK wants Russia to hand over businessman Andrei Lugovoi, whom UK investigators suspect of murdering Mr Litvinenko - he died after being given a fatal dose of radioactive polonium 210.
Russia refused to extradite Mr Lugovoi, now a member of the Russian parliament, so Britain expelled four Russian diplomats - Moscow then expelled four British diplomats.