The UK recording industry is urging the foreign secretary to raise the issue of Russian bargain music download website allofmp3.com at the G8 summit.
The website offers Keane's number one album for less than a pound
The British Phonographic Industry (BPI) trade group wants Margaret Beckett to discuss the site with Russian President Vladimir Putin in St Petersburg.
The BPI is suing the website, claiming it is breaking UK law by selling music there without the necessary licence.
Allofmp3.com says it operates "in full compliance with all Russian laws".
BPI Chairman Peter Jamieson said he had written to Mrs Beckett, asking her to "urge the Russian government to take action against the operators of the site by insisting that it is removed from the internet".
His letter adds that "President Putin has clearly stated his commitment to protecting intellectual property rights".
Allofmp3.com offers downloads for as little as five pence, and a survey has suggested it is the UK's second most popular download site, accounting for 14% of downloads.
The site says it is licensed by the Russian Multimedia and Internet Society (Roms) and the Rightholders Federation for Collective Copyright Management of Works Used Interactively (Fair).
Its operators say it "regularly transfers substantial amounts of royalties" to Russian copyright organisations.
But the BPI says "no money flows back to artists or record companies in the UK".
The International Federation of the Phonographic Industry (IFPI) says the Roms licence is not legitimate and it would not cover consumers in other countries even if it was.