After a consultation process that has divided the telecoms and media industries, the Business Secretary indicated he was ready to push forward with the proposal.
People would only be cut off from the internet after ignoring two prior warnings, however, and there would be an appeal process for those targeted.
Lord Mandelson said the power, to be introduced under the Digital Economy Bill, would be used as a 'very last resort' and would only affect 'persistent rule breakers'.
Unlawful file-sharing costs the music, film and other creative industries millions of pounds a year.
Speaking at a creative industries conference in Hertfordshire, Lord Mandelson said: "It's clear that whilst unlawful file-sharing excites a strong response from all sides, it is not a victimless act.
Threat
"It is a genuine threat to our creative industries.
"The creative sector has faced challenges to protected formats before.
"But the threat faced today from online infringement, particularly unlawful file-sharing, is of a different scale altogether. We cannot sit back and do nothing."
Under the proposed legislation, there would be reserve powers to instruct internet service providers to take 'technical measures' against illegal file-sharers.
Measures could also include slowing down internet connections as an alternative to cutting off users altogether.
Ministers also indicated they wanted to modernise copyright laws so they reflected 'reasonable' behaviour which was not damaging to creative industries.
That would include allowing people to copy a CD on to their iPod or share it with family members - both of which are currently illegal.
Mashing-up content
The move follows a review by intellectual property minister David Lammy, who said: "This is not an excuse to infringe copyright through unlawful file-sharing, but is about being able to do more with legally obtained content, such as remixing music and mashing-up content to create grime and hip-hop tracks.
"I don't want to see a regime based on arbitrary rules, but a system that recognises how consumers behave at a time when we rely increasingly on technology in our everyday lives."
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Black Flag (28/10/2009 at 15:41)
A ridiculous idea in itself, but the fact that it is boomerang man Peter Mandelson who is trying to promote a "three strikes" policy makes it truly hilarious.
This proposal breaches the most basic principles of the rule of law and as such, should be ignored by anybody who has any respect for the rule of law.