The matter is expected to be raised by Tony Blair when he meets the Russian President Vladimir Putin at the two-day summit, which is supposed to improve relations between the world's largest country and the 25-nation bloc.
Prosecutors in St Petersburg, where the British Council has one of its 15 Russian offices, said they had opened a criminal investigation aimed at proving that the council owed the government "millions" in back taxes. They also claimed that the council, which offers English language courses, had no permit to be engaged in educational activity.
The prosecutors insisted that news of their investigation was not timed to coincide with Mr Putin's visit to Britain.
"There is evidence of a violation of Russian legislation and so there can be no question of any international politics," St Petersburg's main investigation directorate told the Interfax news agency.
"A criminal case regarding illegal entrepreneurship is being pursued in connection with the offering of commercial English language courses. Also over the past four years the British Council has not paid a single kopeck in tax from its commercial activity."
The Russian foreign ministry rejected any link between today's summit and the case, arguing that efforts to link the two were "a blatant attempt simply to misinform public opinion on the issue ... [and] the timing of the case's opening".
It is not the first time that the British Council has found itself at the centre of a diplomatic dispute in Russia. The Russian tax authorities made a series of similar claims against the organisation last year, causing a furore that was eventually defused in a one-to-one meeting between Mr Blair and Mr Putin at the G8 summit. The UK has repeatedly argued that the British Council is registered as a charity in England and ploughs all its profits back into projects in Russia.
A spokeswoman for the council told The Independent that the organisation was "surprised" by the allegations of the prosecutors. "We have made all the back-tax payments and are working in complete compliance with Russian law," she said.
The Moscow office had been officially registered last May, she added, and the St Petersburg branch in August, and the council had always co-operated with official inquiries.
One Russian daily newspaper - owned by Boris Berezovsky, a British-based Russian tycoon who is a fierce critic of Mr Putin - claimed the dispute was orchestrated by the Kremlin and a product of Moscow's uneasiness about a British government initiative to pour £1m into educational projects in the troubled North Caucasus region, where Chechnya is located. The money is being managed by the British Council but Moscow is said to want some oversight in a part of the world where it is extremely sensitive to foreign interference. Britain's continued failure to extradite two men regarded in Moscow as criminals - the Chechen envoy Akhmed Zakayev and Mr Berezovsky - is a further obstacle to better bilateral relations.
Despite these differences, Mr Putin became, in 2003, the first Russian leader to pay a state visit to Britain since 1874, and the UK remains one of the biggest foreign investors in the Russian economy.