The proposed law comes as intelligence agencies and police grapple with monitoring terrorist activity online amid a debate sparked by Edward Snowden over government access to personal data online.
Home Secretary Theresa May told the BBC that the measures would not ban encryption and "will not be giving powers to go through people's browsing history".
However, the authorities will be able to look at Internet and social media activity if they get a special warrant.
Such warrants are currently issued by May but this authority could be handed to judges under the new measures.
Technology companies will reportedly have to keep records of emails and people's use of social media sites like WhatsApp and Facebook for 12 months and authorities will be able to access this with a second warrant.
The disclosures came ahead of Wednesday's release of the draft Investigatory Powers Bill.
It will be scrutinised by a committee of lawmakers, allowing changes to be made before it is formally debated by parliament.
Britain's intelligence chiefs have issued a string of warnings in recent months about the dangers posed by terrorist organisations recruiting and planning attacks online.
In a rare public speech last week, the head of domestic spying agency MI5 Andrew Parker said Britain was under threat "on a scale and at a tempo that I have not seen before".
He highlighted the Islamic State (IS) group's "sophisticated exploitation of technology" through "the full range of modern communications tools to spread its message of hate and to inspire extremists".
The previous coalition government led by Prime Minister David Cameron wanted to pass a law covering similar issues, dubbed a "snoopers' charter" by critics, but was blocked by junior coalition partners the Liberal Democrats as too intrusive.
Since winning May's general election outright though with a small majority, Cameron has more room for manoeuvre but is still likely to face opposition from some in his Conservative party over the measures.