Parliament's intelligence and security committee (ISC) is to mount an inquiry into whether the laws on "state snooping" on private communications are adequate to regulate Britain's spy agencies in the internet age.

The committee's chairman, the former foreign secretary Sir Malcolm Rifkind, said that it had decided to mount a wider investigation into the legal framework surrounding the interception and surveillance of communications in the face of widespread public concern over "snooping" by intelligence agencies on both sides of the Atlantic.

Rifkind said the intelligence agencies "can only operate under acts of parliament" and that it was appropriate for his committee to "give a considerable amount of thought to the wider legislative framework".

He said: "We don't start at this stage with any presupposition that there is a problem. We simply say that it is appropriate that it should be looked at."

The wider review comes after the ISC's report cleared the Government Communications Headquarters (GCHQ) of "circumventing" UK law in any way, relying on unpublished policies and procedures the agency had put in place to ensure that its role in the intelligence-sharing programme with the Americans complied with the Human Rights Act.

The ISC, confirming Britain's use of surveillance material obtained from the US Prism programme for the first time, said it had reviewed a list of UK nationals or residents who had been subject to monitoring as a result of the sharing arrangement with the US National Security Agency (NSA).

The committee members also saw the warrants under which the individuals were targeted.

The ISC also cleared GCHQ of illegal conduct in its access to the Prism programme, which gave American intelligence a window on the daily communications made by millions of people around the world.

The document concluded: "It has been alleged that GCHQ circumvented UK law by using the NSA's Prism programme to access the content of private communications. From the evidence we have seen, we have concluded that this is unfounded."

However, the committee added under the heading "next steps" that, "it is proper to consider whether the current statutory framework governing access to private communications remains adequate".

The committee said it was "examining the complex interaction between the Intelligence Services Act, the Human Rights Act and the Regulation of Investigatory Powers Act [Ripa], and the policies and procedures that underpin them, further."

NSA documents seen by the Guardian showed that "special programmes for GCHQ exist for focused Prism processing" and that the British agency had generated 197 intelligence reports from Prism in the year to May 2012. The documents, leaked by NSA whistleblower Edward Snowden, also show that legal constraints designed for an era in which electronic surveillance involved attaching crocodile clips to copper telephone wires had not been updated for an age in which fibre-optic cables carry the traffic of millions of internet users. In one 2011 presentation, a GCHQ legal adviser told NSA analysts: "We have a light oversight regime compared with the US."

Under a little known clause in Ripa, GCHQ is permitted to collect vast amounts of data under a single warrant or a special certificate issued by the foreign secretary.

Rifkind confirmed at a press briefing after publication of the report that the short investigation had only focused on intelligence information that GCHQ had specifically requested from the US on particular warranted suspect individuals. The committee had not looked at the legality of personal data on British citizens or individuals in Britain that might been offered by the NSA to the UK security services.

Nor, Rifkind added, had the committed looked at what happened if US agencies offered information to the UK – a question that he said might be considered as part of a further stage of the ISC inquiry.

The short inquiry had also concentrated only on the content of private communications that had been intercepted, not the communications "metadata" that has also been harvested by the NSA's Prism programme.

Rifkind also agreed that the three key pieces of legislation - the Intelligence Services Act, the Human Rights Act and Ripa – were all at least 13 years old now and drawn up in a pre-digital age.

But he added that just because a law was passed some time ago, that did not mean that it was not still relevant.

William Hague, the foreign secretary, welcomed the report. "I see daily evidence of the integrity and high standards of the men and women of GCHQ. The ISC's findings are further testament to their professionalism and values," he said.

But Shami Chakrabarti, director of Liberty, said: "The painfully careful words of the ICS's report clear absolutely nothing up. There's nothing to allay fears that industrial amounts of personal data are being shared under the Intelligence Services Act, and concerns that all UK citizens are subject to blanket surveillance under GCHQ's Tempora programme aren't even mentioned. This spin-cycle is marked 'whitewash'."

Her concerns were echoed by Nick Pickles of Big Brother Watch: "If the law is not fit for purpose, the question of not breaking it is largely irrelevant.

"These laws were written when the internet was unknown to the majority of people and was far from the minds of the parliamentarians who drafted the laws GCHQ is now bound by, many years on.

"When the ISC is raising concerns that the current legal framework is adequate, alarm bells should be ringing loud and clear that all is not well. Parliament must urgently turn its attention to this issue," he said.