Therea May is coming under pressure to launch an investigation into claims the the UK Government Communications Headquarters (GCHQ) has been covertly gathering data from some of the world's largest internet firms through a US spy programme called Prism.

Labour's Keith Vaz, the Chairman of the Commons Home Affairs Committee, said the allegations regarding the UK's Cheltenham-based electronic listening post were chilling and appeared to be "the snooper's charter by the back door".

LibDem backbencher Julian Huppert, who also sits on the committee, said he hoped to force the Home Secretary to make a Commons statement on the matter on Monday.

Last night, Yvette Cooper, the shadow home secretary, stressed that counter-terrorism intelligence gathering was important, but made clear there had to be legal safeguards, "including proper protection for British citizens' privacy, proper oversight and checks and balances to make sure intelligence powers are not misused".

She called on Prime Minister David Cameron to tell Westminster's Intelligence and Security Committee "what ministers know" about Prism.

It is claimed leaked documents show GCHQ has had access to Prism, set up by America's National Security Agency, since June 2010.

They allegedly show the Prism programme appeared to have allowed 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.

Last night, GCHQ refused to comment directly on the claims it had been using Prism, but stressed it took its legal obligations very seriously.