The decision follows complaints about the workability of the legislation, aimed at cracking down on ninternet pirates, according to the BBC.
The UK government committed itself to tackling the problem of illegal peer-to-peer file-sharing in the Digital Economy Bill.
The website-blocking legislation was given the thumbs-down in submissions to the Your Freedom website, set up to gauge public opinion on laws and regulations.
Deputy prime minister Nick Clegg said the government will look at whether it has the right tools to address the problem of online copyright infringement.
Culture secretary Jeremy Hunt has now asked telecoms regulator Ofcom to consider the viability of blocking websites, particularly those used exclusively for facilitating illegal content downloads.
The questions to be considered by Ofcom include whether it is possible for access to sites to be blocked by internet service providers, how robust such blocks would be, whether specific parts of a site be blocked, and what it would cost ISPs to implement such blocks.
The Open Rights Group, which has long campaigned against the DEA, has welcomed the news of Ofcom's review.
According to the group, the DEA introduces many measures that will impede many businesses and ordinary users who make use of the internet.