The agency can tap into and store the data for as long as 30 days so it can be analysed under an operation codenamed Tempora, according to the Guardian.
Cheltenham-based GCHQ would not comment on intelligence matters but insisted last night it was “scrupulous” in complying with the law.
The newspaper said data, including phone calls and a user’s internet history, is shared with the US National Security Agency (NSA).
Mr Snowden, a former US government intelligence analyst who fled to Hong Kong, said: “The UK has a huge dog in this fight. They (GCHQ) are worse than the US.”