Prime Minister David Cameron has been urged to launch an investigation into allegations that Britain's electronic listening post GCHQ has been gathering data through a secret US spy programme.
Labour's Keith Vaz said the claims were "chilling" and shadow home secretary Yvette Cooper demanded an inquiry.
According to The Guardian, GCHQ had access to data covertly gathered from leading internet firms in the US.
GCHQ said it operated within a "strict legal and policy framework".
The Guardian says it has obtained documents showing that the secret listening post had access to the Prism system, set up by America's National Security Agency (NSA), since at least June 2010.
The documents were said to show that the British agency had generated 197 intelligence reports through the system in the 12 months to May 2012 - a 137% increase on the previous year.
The newspaper said that the Prism programme appeared to allow GCHQ to circumvent the formal legal process required to obtain personal material, such as emails, photographs and videos, from internet companies based outside the UK.
GCHQ takes its obligations
under the law very seriously.
Our work is carried out in
accordance with a strict legal
and policy framework which
ensures that our activities are
authorised, necessary and
Mr Vaz, the chairman of the Commons Home Affairs Committee, said: "I am astonished by these revelations which could involve the data of thousands of Britons.
"The most chilling aspect is that ordinary American citizens and potentially British citizens too were apparently unaware that their phone and online interactions could be watched.
"This seems to be the snooper's charter by the back door. I shall be writing to the home secretary asking for a full explanation."
Ms Cooper called on the prime minister to ask a powerful committee of MPs and peers to investigate "the UK's relationship with the Prism programme, the nature of intelligence being gathered, the extent of UK oversight by ministers and others, and the level of safeguards and compliance with the law".
The Intelligence and Security Committee, which oversees the work of MI5, MI6 and the Government Communications Headquarters (GCHQ), should be fully briefed on the subject by "the prime minister, home secretary and foreign secretary, and all the intelligence agencies", she said.
This needed to happen "as swiftly as possible," she argued.
The committee is appointed by, and reports to, the prime minister.
"It is important for the UK intelligence community to be able to gather information from abroad including from the United States particularly in the vital counter terror work they do," the Labour frontbencher added.
"However there also have to be legal safeguards in place, including proper protection for British citizens' privacy, proper oversight and checks and balances to make sure intelligence powers are not misused.
"And the public need confidence that their privacy is being properly respected and protected."
The UK's data protection watchdog, the information commissioner's office (ICO), also raised concerns about the report.
"There are real issues about the extent to which US law enforcement agencies can access personal data of UK and other European citizens," the watchdog said in a statement.
"Aspects of US law under which companies can be compelled to provide information to US agencies potentially conflict with European data protection law, including the UK's own Data Protection Act.
"The ICO has raised this with its European counterparts, and the issue is being considered by the European Commission, who are in discussions with the US government."
GCHQ issued a statement in which it did not deny The Guardian's story.
A spokesman for the agency, based in Cheltenham, said: "GCHQ takes its obligations under the law very seriously.
"Our work is carried out in accordance with a strict legal and policy framework which ensures that our activities are authorised, necessary and proportionate, and that there is rigorous oversight, including from the secretary of state, the Interception and Intelligence Services Commissioners and the Intelligence and Security Committee."
US spies have been accused of tapping into servers of nine US internet giants including Apple, Facebook, Microsoft and Google in a giant anti-terror sweep. All deny giving government agents access to servers.
But the Prism programme has been strongly defended by James Clapper, director of US national intelligence.
And President Barack Obama said it was closely overseen by Congress and the courts and that his administration had struck "the right balance" between security and privacy.
He also stressed that the surveillance of phone call "metadata" did not target US citizens or residents and government agencies were not listening to telephone calls.
But civil liberties campaigners in the UK have said they are deeply concerned about the allegations.
Lib Dem MP Julian Huppert, a long standing campaigner against the government's proposed Communications Data Bill - dubbed a "snooper's charter" by critics - said he would "raise the issue as soon as possible in Parliament".
The data bill, which would have authorised the retention of every UK citizen's web browsing records, was dropped because the Lib Dems did not support it.
But the home secretary has talked of its importance to national security, following the killing of Drummer Lee Rigby in Woolwich.
Nick Pickles, director of privacy and civil liberties campaign group Big Brother Watch, said: "There are legal processes to request information about British citizens using American services and if they are being circumvented by using these NSA spying arrangements then that would be a very serious issue."
He added: "If British citizens have had their emails and social media messages seized by the US government without any justification or legal authority, serious questions must be asked at the highest levels."