Relations between London and Moscow threatened to plummet to a post-cold war low yesterday amid renewed Russian demands for action against Boris Berezovsky over the tycoon's claim that he is plotting to overthrow Vladimir Putin.

The Russian ambassador to the UK warned that bilateral relations would inevitably suffer if prompt action was not taken against the Britain-based multi-millionaire, who told the Guardian that he was fomenting a revolution to topple Mr Putin by force.

Yesterday it also emerged that British authorities have begun a second inquiry into Mr Berezovsky's comments, with the Home Office's border and immigration agency investigating whether they could undermine his refugee status. Scotland Yard's counter-terrorism command is already assessing whether he breached anti-terrorism laws by inciting a coup.

But it was the remarks of the Russian ambassador, Yury Fedotov, that will have alarmed Downing Street at a time when ministers and senior officials are increasingly concerned about Russia's assertiveness on the international stage.

Speaking at the embassy in west London, Mr Fedotov said he had sent a letter on Wednesday to John Reid, the home secretary, underlining the seriousness with which the issue was viewed in Moscow. He also enclosed a copy of a warrant for the arrest of Mr Berezovsky signed by Yury Chaika, the Russian prosecutor general.

"A speedy resolution would help to improve, to develop, our relations even further," he said. "But absence of a reaction would have some impact on bilateral relations" and create a "new situation".

The dispute could have a serious impact on bilateral relations, analysts said yesterday. Moscow is at odds with Britain on many issues, including how best to curb Iran's suspect nuclear programme and plans to grant Kosovo independence.

Tensions also surround British-backed western efforts to promote democratic institutions in countries of the post-Soviet "near abroad" such as Georgia and Ukraine, US-led plans for European missile defence, and Nato's eastward expansion. "The Russians are already causing trouble across the board. This could just make them behave even worse," one former official said.

But David Clark, a former Foreign Office adviser, said it would be a mistake to concentrate on possible Kremlin retaliation. "The government is very worried about the impact of this dispute on bilateral relations - excessively so," said Mr Clark. "It would be a mistake to try to mollify the Kremlin instead of being honest and clear about the reasons why no British court is likely to support the extradition of its political opponents. The reason is that there is, in current circumstances, little possibility of a fair trial."

At the Home Office, sources confirmed yesterday that immigration officials were investigating whether Mr Berezovsky's comments had broken UK laws and regulations and altered his refugee status.

Immigration law experts agreed that the Home Office may struggle to strip Mr Berezovsky of asylum status, granted under the 1951 UN refugee convention, unless they establish that he is "guilty of acts contrary to the purposes and principles of the UN", as laid down by the convention. Ministers believe they may be able to review his status if they consider his presence here is no longer conducive to the public good.

Although Mr Putin has said he would stand down when his second elected term comes to an end next year, as required by the constitution, Mr Berezovsky told the Guardian he believed the Russian president could be removed only by force.

"We need to use force to change this regime," he said, in comments which appeared calculated to infuriate the Kremlin. "It isn't possible to change this regime through democratic means. There can be no change without force, pressure."

He claimed to be in contact with like-minded people in the country's ruling elite, offering financial assistance as well as "my understanding of how it could be done". When asked whether he was fomenting a revolution, he said: "You are absolutely correct."

Mr Berezovsky added that he was confident his refugee status could not be revoked, and that his position was even stronger since the poisoning of his former employee Alexander Litvinenko. He has consistently denied the charges laid against him in Russia and says they are politically motivated. The 61-year-old billionaire was in Israel last night, where he said he travelled on business. He said he planned to return to the UK today, and had no comment on the diplomatic furore.

Mr Berezovsky made his estimated £850m fortune during Russia's 1990s rush to privatise, by capturing state assets at knockdown prices. Two previous attempts to extradite him failed. He was granted asylum in 2003 after claims by Litvinenko, a former Russian intelligence agent, that the Kremlin had ordered the tycoon's murder.