The move comes a year after the search giant was warned by the then culture secretary Jeremy Hunt that new laws would compel it to demote such sites if it did not act first.
Now the department for culture, media and sport (DCMS) says it will examine the technical changes promised by Google in August, when it pledged to relegate sites that persistently flout copyright laws.
A spokesman for the DCMS said the government would "consider our options" following the review, raising the prospect of fresh legislation that would force Google to downgrade pirated material in search results.
Entertainment groups, comprising the film, music and publishing industries, complained that top Google search results remain dominated by pirate sites despite repeated assurances from the internet firm that it would push them down.
Government ministers see Google as central in the fight against online piracy because it is the main portal to the web for nine out of 10 Britons. The former culture secretary Jeremy Hunt privately threatened Google in September 2011 that he would introduce legislation to force it to take action against well-known pirate sites if the company did not take action voluntarily.
But even today, music fans who search Google for their favourite artist – for example "Katy Perry download" or "One Direction MP3" – will find the highest-ranked results point them to illegal filesharing sites.
Several of the most complained-about websites – most of which are listed by Google in its own transparency report – still appear prominently in search results for artists and films.
For example, the top search result for "Coldplay MP3" is for the website BeeMP3.com, which has received almost 400,000 copyright complaints from music groups according to Google's report. A search to stream the new James Bond film, Skyfall, also links to apparently infringing sites.
Google maintained that it was taking action against piracy websites and had demoted millions of sites every month.
A spokesman for Google said: "We continue to work closely with the industry to protect rights holders and their material. Sites with high numbers of removal notices are now more likely to appear lower in our results, we've made it easier to report pirated material and now take down more than seven million infringing links per month."
However, entertainment groups complained that Google was still not doing enough to tackle the issue.
Geoff Taylor, chief executive of the BPI, said: "Google said it would stop putting the worst pirate sites at the top of search results. Google's transparency report shows they know clearly which are most infringing domains. Yet three months into the much-vaunted algorithm change, many of these illegal sites are still dominating search results for music downloads.
"We are talking to Google to try to establish why this is the case. With the launch of music in Google Play, now is the time to build a genuine partnership and for Google to show the world that it loves music. This means Google must stop dragging its feet and giving profile to illegal sites that it knows rip off everyone working in music."
Richard Mollet, chief executive of the publishing industry trade body the Publishers Association, said he welcomed Google's promise to demote infringing sites, but added: "We are yet to see evidence for a significant reduction in their presence in search results."
Kieron Sharp, director general of the Federation Against Copyright Theft, added: "Google claims to have taken steps to make infringing websites and the pirated content they promote less accessible, yet it seems that its search engine is still promoting these sites which are often making money from advertising or other payment mechanisms."
The way Google ranks piracy sites came to a head last year when Hunt told Google he would introduce new laws as part of the forthcoming Communications Act if the internet firm did not take immediate action. Hunt, now health secretary, was replaced by Maria Miller as culture secretary, as part of David Cameron's cabinet reshuffle in September.
A spokesman for the DCMS did not rule out the prospect of fresh legislation to force Google to take urgent action on copyright.
The DCMS said in a statement: "The Department is aware of the concerns raised by rights holders that this has not had the impact that they hoped, and, together with industry, we now need to review the effect of the technical change made by Google and consider our options.
"This is part of a wider campaign to tackle online infringement, which includes working together with payment facilitators (such as credit card companies) and online advertising bodies to reduce the revenue flowing to seriously infringing – often criminal – sites."
It is understood that the government will meet with Google, internet service providers, and rights holders before Christmas to discuss online piracy.
The DCMS is due to set out its policies on the creative industries as part of the Communications Review white paper to be published in early 2013.
Google's tough stance on its search results has been a major sticking point in its attempt to strike music licensing deals with the industry as it attempt to take on Apple's iTunes.
The company says it received reports of 7.6m infringing web addresses in the past month – a sign of the significant scale of the problem.
Google has fought attempts to make it remove websites that have proved to be infringing entirely from its search results, arguing that this would amount to an attack on freedom of expression. The internet firm has stressed that downgrading websites was not a "silver bullet" in the fight against piracy, and pointed out that there are comparatively few legal services to replace the illicit sites in search results.
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