UPDATE: Edward Snowden, the NSA whistleblower, has been charged with espionage by the United States.
The agency is able to tap into and store data from the cables for up to 30 days so it can be analysed under an operation codenamed Tempora, the Guardian reported.
The Cheltenham-based agency would not comment on intelligence matters but insisted it was "scrupulous" in complying with the law. The newspaper said there were two principal components to the agency's surveillance programme, called Mastering the Internet and Global Telecoms Exploitation.
It claimed the data was shared with the organisation's US counterpart the National Security Agency (NSA). The information is the latest leak from Snowden, the NSA whistleblower responsible for a string of disclosures about US intelligence operations.
The newspaper claimed Operation Tempora had been running for 18 months and GCHQ and the NSA are consequently able to access vast quantities of communications between entirely innocent people, as well as targeted suspects, including phone calls, the content of email messages, Facebook entries and a user's internet history.
Snowden, who fled the US for Hong Kong after deciding to reveal the NSA's secrets, told the Guardian he wanted to expose "the largest programme of suspicionless surveillance in human history. It's not just a US problem. The UK has a huge dog in this fight," he said. "They (GCHQ) are worse than the US."
The Guardian reported that GCHQ lawyers told US counterparts there was a "light oversight regime" in Britain compared with America. The newspapers said the documents revealed that by last year GCHQ was handling 600 million "telephone events" each day, had tapped more than 200 fibre-optic cables and was able to process data from at least 46 of them at a time.
The intelligence gathered is understood to have contributed to a number of arrests and convictions including a terror cell in the Midlands who were jailed for planning co-ordinated attacks. It is also claimed to have led to the arrest of five Luton-based individuals preparing acts of terror, and three London-based people planning attacks prior to the Olympics.
A source with knowledge of the work of the intelligence agencies said: "It's not about going through everybody's emails or phone calls. It's about homing in on criminal activity in order to lead the intelligence agencies to be able to take action."
The source said the vast majority of the data gathered was discarded, with the agency focused on the "needles" of relevant information within the "haystack" of material. The source said: "What they do is scan the haystack of bulk data for any needles that could have national security implications. All the rest gets discarded and is not looked at. The vast bulk of the data is not looked at in any detail."
The "needles" are logged and the reason for holding any information has to be justified, the source said. The logs are regularly audited and subject to scrutiny by the Interception of Communications Commissioner. A ministerial warrant authorised the process of scanning the data and the work was done in a "proportionate and legal way", the source said.
Privacy campaign group Big Brother Watch's director Nick Pickes 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. Britain has a clear legal process in place to govern the interception of the content of communications and blanket interception is not a part of that system.
"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. This question must be urgently addressed in Parliament.
"The fact GCHQ staff have been discussing how light the UK's oversight regime is compared to the US highlights why we need a wholesale review of surveillance law, including the fact that there is absolutely no judicial process within the current system and the people making these decisions are able to hide in the shadows rather than face public scrutiny."
A GCHQ spokeswoman said: "We do not comment on intelligence matters. Our intelligence agencies continue to adhere to a rigorous legal compliance regime. GCHQ are scrupulous in their legal compliance."
Reports suggested a private plane was on standby to transport Snowden from Hong Kong to Iceland. Businessman Olafur Vignir Sigurvinsson said that while he has not spoken directly to Snowden, he has been in touch with a third party representing him and had access to planes in Hong Kong and the Chinese mainland.