Intellectual property minister David Lammy said the idea had been scrapped because the legal issues involved were too complex.
Lammy, speaking to The Times in advance of the publication of a report on the future of Britain's digital industries, said the music industry and ISPs have yet to agree on how best to deal with online music piracy.
The MP also said that illegal downloaders should not be arrested.
ISP British Telecom said in a statement: "We're still hopeful that an amicable solution, without the need for legislation, can be reached."
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