Politicians as well as officials were linked to such corruption and often gave protection to Russia's powerful crime gangs, the spokesman, Toby Latta, said on BBC2's The Money Programme.
"It was made clear through intermediaries to our client that the signature of this official would be applied to the agreement upon payment of a seven-figure sum into a foreign bank account. And if that money was not paid the signature would not be applied."
The official was not identified. The British company refused to pay and its deal collapsed.
Russia, which has a heavy burden of international debts, has suffered a loss of investor confidence as corruption, violence and instability have led overseas companies to stay away or pull out.
Last month, after a police raid, a Swiss construction company, Mabetex, involved in a contract to refurbish the Kremlin, was accused of paying credit card bills for Boris Yeltsin, the Russian President, and his two daughters and bribing a government estates manager.
The Kremlin and Mabetex denied wrong-doing.
American money-laundering investigators are said to have subpoenaed records from companies linked to the husband of President Yeltsin's daughter Tatyana Dyachenko.
The Russian mafia is believed to have illegally channelled up to pounds 6bn out of the country via banks in London and the US, including money from pounds 2.6bn of International Monetary Fund loans meant to help Russia's struggling market economy.Reuse content