State Duma legislator Nikolai Kovalyov, a former director of the
Federal Security Service, or FSB, made the comment on NTV television, Interfax said.
Less than a week ago, the FSB accused four British diplomats of spying and said one of them had provided money for non-government organisations - an espionage scandal dismissed by Kremlin critics as part of a campaign to discredit NGOs.
It was unclear whether Mr Kovalyov was referring to British or Russian citizens. Diplomats have immunity from arrest.
A duty officer at the Federal Security Service, the Soviet KGB's main successor, said the agency could not comment.
Correspondents at NTV said a portion of a program featuring Mr Kovalyov was aired as a teaser but that the show would be broadcast on Sunday, and they could not confirm the content of his comments.
British Embassy officials could not be reached for comment.