The plan to cut off persistent pirates has proved controversial
The government has published a new draft of a controversial clause in the Digital Economy bill, in an effort to ease its progress through parliament.
The Liberal Democrats said they will oppose any plans to rush the Digital Economy bill into law.
The bill faces its second reading in the House of Commons next week.
Critics say the bill is unnecessarily draconian, particularly plans to cut off persistent net pirates and grant powers to block access to some sites.
Clause 18 has proved one of the most controversial aspects of the bill.
Originally it outlined how the government intended to future-proof the legislation by granting it the power to deal with other methods of copyright infringement, including the right to block access to websites, without the need for further legislation.
The new clause steps back from this, granting "limited power to propose regulations in the future".
It would "allow copyright owners to apply for court injunctions requiring service providers to block access to specified internet locations providing access to copyright infringing material".
But, before such injunctions could be carried out, the Secretary of State would have to consult "widely with industry", said a spokesman for the Department for Business, Innovation and Skills.
He or she would also need to be satisfied that the new form of copyright theft was having a serious affect on the industry, of equivalent severity to the current trend for file-sharing via peer-to-peer networks, he added.
It is estimated that in 2007, one billion music tracks were shared illegally. More than half of all net traffic in the UK is believed to be content being shared illegally.
It is widely expected that the Digital Economy bill will enter the so-called "wash-up" process.
This sees remaining government legislation speeded up ahead of a general election.
The Liberal Democrats have called for the bill in its present form to be scrapped and re-introduced in the next parliament.
The Open Rights Group, which has orchestrated a campaign against the bill, said any attempt to rush the legislation through would be "undemocratic".
"It is outrageous to circulate the text of a clause days before it is due to be debated," said spokesman Jim Killock.
"There will be no scrutiny and it will be rushed through the day after. This is no way to make serious, wide-ranging laws," he added.
The fate of the bill will rest with MPs.
"A rising number of MPs, including the speaker of the House of Commons himself, are concerned about the lack of scrutiny and the future of the bill is by no means certain," said Mr Killock.
Some 20,000 people have written to their MPs voicing their opposition to the bill.
Hundreds protested outside parliament last week and campaigners are planning a series of advertisements designed to block its progress.
The Stop the Digital Economy Bill campaign is being organised by the Open Rights Group and digital campaigners 38 Degrees.
They have raised £20,000 to run ads in national newspapers and websites on 6 April.
That is the day when Gordon Brown is expected to announce the general election and also the day when the digital economy bill is due to be debated in the House of Commons.