The lawmakers believe that Google could have done more to comply with ex-Formula One boss Max Mosley's request to take down links to a video of a "sick Nazi orgy", covertly produced by the News of the World, which were widely distributed on the net after 2008.
In an ill-tempered evidence session in January, Google's legal director Daphne Keller told the committee that removing the offending material was not an easy task.
"We don't have a mechanism that can find duplicates of pictures or duplicates of text and make them disappear from our web search," she said at the time. "And as a policy matter I don't think that would be a good idea."
However, the cross-party committee said that Google's argument was "totally unconvincing", and urged the search firm to introduce an algorithm for promptly removing search links found to be in breach of privacy.
The committee was asked by the government to investigate privacy and free speech issues after a series of high-profile super injunctions were breached online last year.
They included a case in which Ryan Giggs was 'unmasked' at least 75,000 times on Twitter as being behind a gagging order preventing newspapers from publishing details of his alleged affair.
The report said that online services including Twitter and Facebook must be brought in line with offline media such as newspapers in cases such as this.
"We recommend that, when granting an injunction, courts should be proactive in directing the claimant to serve notice on internet content platforms such as Twitter and Facebook," it said.
But the committee's sternest words in the report were reserved for Google.
Mosley, who won £60,000 in damages in a privacy case against the now-defunct News of the World, sued Google over the proliferation of links to the video online, claiming that the search giant "could stop a story appearing, but don't or won't as a matter of principle".
This came after he had been forced to spend more than £500,000 in legal fees to pursue individual take-down orders for links to the "orgy" video posted on the web.
"Where an individual has obtained a clear court order that certain material infringes their privacy and so should not be published, we do not find it acceptable that he or she should have to return to court repeatedly in order to remove the same material from internet searches," the report said.
Mosley told the MPs that he confronted Google about the situation, saying: "Here are the pictures. We know which ones they are. Simply programme your search engine so they don't appear."
But Google argued that while it could create such algorithms to filter search results, it would not be ethical to police the net in such a way.
The committee, however, was unmoved by that stance.
"Google acknowledged that it was possible to develop the technology proactively to monitor websites for such material in order that the material does not appear in the results of searches," said the committee's report.
"We find their objections in principle to developing such technology totally unconvincing. Google and other search engines should take steps to ensure that their websites are not used as vehicles to breach the law and should actively develop and use such technology.
"We recommend that if legislation is necessary to require them to do so, it should be introduced."
In a statement issued to the BBC, Google said that it "already removes specific pages deemed unlawful by the courts", but insisted that it should not be used to police the web.
"We have a number of simple tools anyone can use to report such content, which we then remove from our index," the firm said.
"Requiring search engines to screen the content of their web pages would be like asking phone companies to listen in on every call made across their networks for potentially suspicious activity."
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