Russian state TV quoted an official from the security service known as the FSB as saying they would be expelled.
The expulsions come as Prime Minister Keir Starmer visits Washington for talks with President Joe Biden that will include Ukraine's request to use Western-supplied weapons against targets inside Russia.
Starmer said on his way to the US that Britain did not "seek any conflict with Russia".
"Russia started this conflict. Russia illegally invaded Ukraine. Russia could end this conflict straight away," he told reporters on Friday.
"Ukraine has the right to self-defence and we've obviously been absolutely fully supportive of Ukraine's right to self-defence - we're providing training capability, as you know. But we don't seek any conflict with Russia - that's not our intention in the slightest," he said.
The FSB said it received documents indicating the diplomats were sent to Russia by a division of the UK Foreign Office "whose main task is to inflict a strategic defeat on our country", and they were involved in "intelligence-gathering and subversive activities".
Russian state TV said in a report the six diplomats had met independent media and rights groups that had been declared "foreign agents" - a label the Russian authorities have actively used against organisations and individuals critical of the Kremlin.
The British embassy in Moscow did not immediately respond to a request for comment from the Associated Press.
There was no immediate comment from Britain's Foreign Office.
Russian foreign ministry spokeswoman Maria Zakharova said in a statement that "we fully agree with the assessments of the activities of the British so-called diplomats expressed by the Russian FSB. The British Embassy has gone far beyond the limits outlined by the Vienna Conventions."
She said the diplomats were carrying out "subversive actions aimed at causing harm to our people".
Explusions of diplomats - both Western diplomats working in Russia and Russian diplomats working in Western countries - have become increasingly common since Russia invaded Ukraine in February 2022.
Russian news outlet RBC counted in 2023 that Western countries and Japan expelled a total 670 Russian diplomats between the beginning of 2022 and October 2023, while Moscow expelled 346 diplomats in response.
According to RBC, it was more than in the previous 20 years combined.
In May the UK expelled Russia's defence attache in London, alleging he was an undeclared intelligence officer, and closed several Russian diplomatic properties in Britain that it said were being used for spying.
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