The shadow foreign secretary has called for parliamentary and ministerial oversight into the work of GCHQ and other intelligence agencies, over surveillance of electronic communications.

Douglas Alexander's call came after the Guardian revealed that GCHQ has secretly gained access to the network of cables that carry the world's phone calls and internet traffic, and has started to process vast streams of sensitive personal information which it is sharing with its US partner, the National Security Agency.

The Labour MP said: "The latest reports in the Guardian underline the need for effective parliamentary and ministerial oversight of GCHQ and our other intelligence agencies.

"Whilst GCHQ do vital work to keep us all safe from harm, it is also vital that they do so with the legal framework set down by parliament, and with proper safeguards in place to protect people's privacy.

"We urged the intelligence and security committee to look into these issues raised by the Guardian, and their work is now under way. These latest reports reinforce the urgency and importance of the ISC's work on this issue."

Malcolm Rifkind, the chairman of the ISC said that he expected to receive a report from GCHQ in the coming days on its response to the Guardian's allegations.

"Whenever there are allegations about the intelligence agencies, we seek to find out the full facts. We have the power to go into all the highly classified material. We don't have to accept what they say, we can go further into the raw data," he told the BBC's Today programme.

Human rights campaigners were concerned that GCHQ was straying beyond the law. Nick Pickles, from privacy campaign group Big Brother Watch, said: "This appears to be dangerously close to, if not exactly, the centralised database of all our internet communications, including some content, that successive governments have ruled out and parliament has never legislated for.

"If GCHQ have been intercepting huge numbers of innocent people's communications as part of a massive sweeping exercise, then I struggle to see how that squares with a process that requires a warrant for each individual intercept."

Shami Chakrabarti, director of Liberty, said she was shocked by the Guardian's report and accused GCHQ of allowing itself a "very generous interpretation of the law".

"They are exploiting the fact that the internet is so international in nature," she told Today. "And I'm pretty sad in a democracy when all that appears to be holding back the secret state is its physical and technological capability and not its ethics or a tight interpretation and application of the law."