Labour leader Ed Miliband said: "Once again we see a very sensitive issue being spectacularly mishandled by this Government.
"It is unclear what they are proposing. It is unclear what it means for people. It is always going to lead to fears about general browsing of people's emails unless they are clear about their proposals, clear about what they would mean, clear about how they are changing the law.
"And I say to the Prime Minister: he has got to get a grip on this Government. He has got to get a grip on the way his Government operates and the way that policy is made."
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.