Critics argue a parent could be made a criminal for a child's actions
The Digital Economy Bill is aimed at stopping people illegally downloading copyrighted material from the internet.
However, critics of the Bill argue that it could have far greater powers and be used to censor and block free speech by whichever political party is in power.
The Bill was rushed through during the "washout" period before Parliament is dissolved.
It was passed by 189 votes to 47 after concessions were agreed that saw the Government dropping a clause which could have allowed it sweeping powers to block sites.
But the amendment to another clause means that it could still be possible to block a site, if court approval were given first.
MPs who opposed the Bill agreed it was right to do something about illegal downloads - where the copyright is owned by someone else - but said new powers were too far-reaching.
One suggested a search engine even as huge as Google could potentially be blocked.
Technology blogs say the law will be way off the mark.
Tom Watson, Labour MP
It might be that a wi-fi network is being used in a household; you might have a parent who pays for the broadband connection and their children are illegally downloading.The assumption in the current wording is that that parent has authorised the child to infringe copyright.
Techcrunch's Mike Butcher said: "In trying to support the old music industry models and tackle illegal file-sharing, the #DEBill, as it's known on Twitter, is poised to produce a new culture.
"That of legal letters from music industry bodies to ISPs, bewildered householders and, no doubt, an manner of internet companies.
He also argues that valuable sites such as Wikileaks, which carries copyrighted work, could be shut down, blocking information that the public had a right to know.
And paidContent:UK says: "The Bill may have had a few parts stripped out and it may even be a damp squib. But the remaining 76-page Bill is still a wide-ranging piece of media and technology reform."
Labour's former digital engagement minister Tom Watson earlier warned of a "catastrophic disaster" with potentially innocent people being cut off because they lived in the same building as illegal downloaders.
"It might be that a wi-fi network is being used in a household; you might have a parent who pays for the broadband connection and their children are illegally downloading.
"The assumption in the current wording is that that parent has authorised the child to infringe copyright."