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."
Yvette Cooper warns 'serious safeguards' needed to protect privacy
Shadow home secretary Yvette Cooper said: "We know that the police and security services who are trying to tackle serious terrorist incidents, of course, need to be able keep up with modern technology.
"We also need serious safeguards in place to protect people's privacy, to make sure there are checks and balances and that nothing is abused."
New monitoring laws 'as soon as parliamentary time allows'
A Home Office spokesperson said: "As set out in the Strategic Defence and Security Review we will legislate as soon as parliamentary time allows to ensure that the use of communications data is compatible with the Government's approach to civil liberties.”
They said it was "vital" police and security services could obtain communications data, including time, duration and dialling numbers of a phone call, or an email address, in certain circumstances.
But added this did not included the content of any phone call or e-mail and "and it is not the intention of Government to make changes to the existing legal basis for the interception of communications."
What the papers say about the Government's surveillance plans
The Guardian: Internet firms warn that government plans to monitor email and social media use in Britain are liable to be used by repressive regimes elsewhere in the world to justify their state surveillance.
Daily Mail: Big Brother plans to spy on all internet visits, emails and texts will cost the taxpayer £2billion.
Daily Telegraph: Government plans to access details of every email and website sent in Britain would be an impractical waste of money that would make the UK more like China and Iran, a leading British technology expert has said.
Govt: Surveillance data 'instrumental in solving crimes'
The Security Minister James Brokenshire has told ITV News that the Government's proposals for monitoring phone calls and online activity is not a "spying exercise" and that the data collected would "instrumental in solving crimes".
Surveillance measures would be 'easy to get around'
Trefor Davies of the ISP firm Timico told ITV News that it would be "easy to get around" the online surveillance measures that the Government is proposing by using mail providers like Google Mail or MSN.
Lib Dem MP: Home Sec may be called to give evidence on surveillance reforms
The Lib Dem MP Julian Huppert, who is a member of the Home Affairs Committee has tweeted that the committee chairman Keith Vaz is considering calling the Home Secretary and head of the Office for security and counter-terrorism (OSCT) to give evidence about the proposed changes to surveillance laws.
Just spoke to Keith Vaz, who Chairs Home Affairs Select C'ttee. He agrees we should call Home Sec and OSCT head in to give evidence ASAP #fb