The proposal forms part of an interim report, Digital Britain. The proposed legislation stops short of forcing ISPs to directly disconnect suspected file-sharers.
"Our response to the consultation on peer-to-peer file sharing sets out our intention to legislate, requiring ISPs to notify alleged infringers of rights (subject to reasonable levels of proof from rights- holders) that their conduct is unlawful," said the report. "We also intend to require ISPs to collect anonymised information on serious repeat infringers (derived from their notification activities), to be made available to rights-holders together with personal details on receipt of a court order."
The Government said that it would soon begin consultation on the proposed new law.
"[The new law] should provide a good evidence base, to make it significantly easier for rights-holders to take targeted legal action against the most significant infringers," said the report. "International experience of action of this sort suggests that more than two thirds of infringers change their behaviour when receiving notification."
The law will create a code on unlawful file-sharing which ISPs would have to sign, and whose enforcement would be carried out by media and telecoms regulator Ofcom.
The Government will also create a new rights agency, which would gather together content creators in different disciplines and encourage them to find ways to prevent piracy and ways to make the legal use of their content more attractive. It would involve creators from the worlds of music, film, television, computer games and software, the report said.
"We think the concept of a new Rights Agency and legislative action aimed specifically at addressing unlawful peer-to-peer file-sharing could be major steps forward," said the report. "But this is new and difficult territory, and we want to get it right. So we will review the impact of any new measures, and will not hesitate to examine other options if these do not prove to be effective."
The report was a wide-ranging look at the state of the UK's technical infrastructure, telecoms connectivity, literacy and content industries as they relate to digital products and services.
The report said that the Digital Britain group will look into whether public subsidies should be used to help extend next-generation broadband networks, and it said that the Government was committed to ensuring that broadband penetration reached the whole of the UK by 2012.
The report also said that it would look into whether a second body should be created to make public service radio and television in competition with the BBC. The basis of the body would be the assets of Channel 4. "It would be a body with public service at its heart, but one which is able to develop flexible and innovative partnerships with the wider private and public sector," said the report.
Ofcom last week proposed that Channel 4 be given an increased obligation to fulfil its public service remit by producing more news and current affairs programmes.