A cross-party committee of MPs and peers has urged the government to consider introducing legislation that would force Google to censor its search results to block material that a court has found to be in breach of someone's privacy.

In a report published today, the joint Commons and Lords committee said Google should proactively monitor its search results, highlighting evidence given by Max Mosley, the ex-Formula One boss who said he had spent at least £500,000 in 23 countries attempting to remove traces of a video filmed covertly by the News of the World from the internet.

Google was criticised by the committee for its "totally unconvincing" objection to requests to filter its search results. The search giant argued that such a policy could threaten the unfettered flow of information online.

The committee was set up by the prime minister in May last year to examine privacy and free speech after the controversy over the increasing use of injunctions, including one taken out by the footballer Ryan Giggs. The report, which has been widely trailed, warns against a new privacy law and sets out recommendations for an "enhanced" press regulator.

The report's most pointed language is reserved for internet companies – such as Google, Facebook and Twitter – which the committee said had presented numerous challenges to the rule of law in the UK.

"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," the committee said. "We recommend that if legislation is necessary to require them to do so it should be introduced."

The committee gave a clean bill of health to high court privacy injunctions, but said that they should routinely apply to websites such as Twitter and Facebook as well as newspapers. They urged the attorney general to be more willing to launch contempt of court claims against internet users if they are suspected of breaching privacy injunctions online, after it was found that the Giggs injunction was tweeted about more than 75,000 times when it finally collapsed in May last year.

In a series of recommendations on the future of press regulation, the committee said the reformed Press Complaints Commission should have the power to fine newspapers and determine the prominence of printed apologies. It urged advertisers to withdraw funding from newspapers and major blogs that opt out of the reconstituted regulator, and threatened "statutory oversight" from a body such as Ofcom if the industry cannot agree a credible package of reforms.

John Whittingdale MP, chair of the committee, said: "The committee spent some time debating whether additional laws to clarify the right to privacy were necessary or desirable.

"However, we concluded that the existing position, where each case is judged by the courts on an individual basis, is now working reasonably well. We are concerned that individuals with grievances about invasion of privacy should have an alternative to costly legal action available to them.

It is clear that media self-regulation under the PCC did not work. We therefore wish to see a stronger self-regulatory system that is seen to be effective and commands the confidence of the public."

A Google spokesman said: "This is a really important issue for which there are no easy answers, particularly when balancing freedom of expression and tackling unlawful content.

"Google already remove specific pages deemed unlawful by the courts. We have a number of simple tools anyone can use to report such content, which we then remove from our index.

"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."