Nick Pickles, director of Big Brother Watch, said: "It's welcome that ministers are now addressing the real concerns people have about being spied upon but a whole range of questions remain unanswered.
"We are still discussing proposals for a huge amount of additional monitoring, so the Deputy Prime Minister's assurances of a full and detailed review are extremely welcome.
"It's still far from clear if this scheme is technically possible or if it will make the public any safer."
Liberal Democrat president Tim Farron vows the party would "kill" proposals for increased monitoring of emails and internet use.
Ministers are preparing a major expansion of powers to monitor the email exchanges and website visits of every person in the UK.