Russian authorities said such broadcasts gave direct support to terrorists.
In the interview with Channel 4 News, shown on Thursday night, Chechen guerrilla commander Shamil Basayev said he planned more attacks like the bloody school hostage-taking he masterminded in Beslan.
Russia, which says Basayev is linked to al-Qaida, had asked London to block the broadcast.
The Russian Foreign Ministry said it deeply regretted the programme had been shown. "We consider this step gives direct information support to terrorists in the North Caucasus," a statement said.
"That this happened in a country that is in the chair of the G8 group of industrial-developed states, where combating terrorism is a key theme, can only arouse concern," it said.
"Today any attempts to justify giving a public platform to terrorists ... with references to freedom of speech look cynical to say the least," it said.
The British government said the decision to air the interview was up to the broadcaster, while adding that Foreign Minister Jack Straw had called the Beslan siege "simply evil beyond reason or excuse".
Basayev said he planned more
attacks similar to Beslan
More than 330 people - half of them children - were killed in that attack.
Britain and Russia have clashed over Chechnya before, when a London court gave asylum to top rebel envoy Akhmed Zakayev.
Russia said Zakayev was an international terrorist, but the court ruled he would not get a fair trial in Russia and allowed him to live freely in Britain.