Lessing, along with playwrights Tom Stoppard and Michael Frayn, complained in a letter to The Times newspaper that the BBC was cutting 19 hours a week of broadcasts from its Russian service and dropping all analytical and cultural features.
"At a time when, in Russia, misunderstanding and mistrust of Britain has reached a height unprecedented since the end of the U.S.S.R., this deliberate reduction in the role of the Russian service seems a perverse concession to those authorities in Russia who have been doing their best to curtail the activities of all British cultural institutions," the letter said.
Ties between Moscow and London sank to a post-Cold War low after Kremlin critic Alexander Litvinenko was murdered with a radioactive substance in London in 2006.
Russia has spurned Britain's demands for the extradition of the chief suspect.
In the dispute that followed, both sides expelled diplomats, and Russia closed down the regional offices of the British government's cultural arm, the British Council.
The BBC said the letter was "misleading" and the planned changes were intended to strengthen the Russian service, particularly to meet growing demand for online content.
"We believe that these changes will help BBC Russian become the most trusted, influential and editorially independent international news provider in Russia," said Nigel Chapman, director of the BBC World Service.
The number of listeners to the Russian radio service has dropped to 730,000 from 1.3 million in 2005, while the number of unique visitors to its web site has grown to more than a million a month, a figure that tripled during the August war between Georgia and Russia.
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