The police and security services are to be given new powers to track suspects through their use of emails, Facebook accounts and Twitter profiles, in controversial legislation to be published on Thursday.
The new details will not be available to local authorities and councils, who are be stripped of their current powers to access information about phone calls, the Home Secretary will announce.
Public bodies will have to apply for the new powers at a later date. The government will foot the bill, the estimated cost of which will be revealed later on Thursday.
However civil liberties campaigners had attacked the legislation as the "most intrusive surveillance regime of any democratic government".
Charles Farr, the director-general of the Office for Security and Counter Terrorism, said more communications were taking place on the internet, with fewer by phone, than ever before.
The new powers were needed to enable police and the security services to get details such as the time of the communication, the sender, the recipient and the location from which the communication was made to help them fight crime and terrorism.
About one in four requests for data by the police and agencies can no longer be met under the current regime, he said.
This could rise to 30% within a few years if no action was taken, he added.
The move comes after Mrs May's initial proposals to extend internet surveillance were greeted with widespread criticism from civil liberties campaigners earlier this year.
The full details will be outlined when the draft Communications Bill is published this morning, on the same day that David Cameron appears before the Leveson inquiry.
Mrs May said: "Communications data is vital for the police in their fight against crime, including serious offences such as child abuse, drug dealing and terrorism.
"These measures are necessary to protect the public and investigate crime - and that is the only reason for which they should be used.
"That is why I think it is right that we look again and ask whether local authorities really need access to communications data."
Tory backbencher David Davis, the former shadow home secretary who challenged Cameron for the leadership of the party, said the plans would be "hugely intrusive".
"It's not content, but it's incredibly intrusive," he told BBC Radio 4's Today programme.
"If they really want to do things like this - and we all accept they use data to catch criminals - get a warrant. Get a judge to sign a warrant, not the guy at the next desk, not somebody else in the same organisation.
"The only people who will avoid this are the actual criminals, because there are ways around this - you use an internet cafe, you hack into somebody's wi-fi, you use what's called proxy servers, and they are just the easy ways."
Farr attempted to reassure civil rights campaigners who have dubbed the legislation "the online snooper's charter" added that, under the proposals, neither the police nor security services would be able to monitor calls, texts, emails or web use in real time and the content of any phone calls or emails would not be covered by the proposals.
He went on: "We are not looking to collect all IP data. We will ask service providers to collect specific services."
Safeguards would be in place at every step, he said.
The measures would theoretically cover any company offering services to people in the UK, regardless of where they were based, he added.
Under the moves, local authorities will not be able to get any of the new powers available to police and the security services under the draft Communications Bill.
Local authorities will also be stripped of their powers under the Regulation of Investigatory Powers Act 2000 to access data relating to phone calls, such as the subscriber's name.
They will be able to apply to Parliament to have these powers reinstated at a later date, but will be barred from accessing the new powers related to emails and internet use.
Public bodies will not automatically get access to the new powers, but will be able to apply for them at a later date.
Assistant Chief Constable Gary Beautridge, the data communications lead for the Association of Chief Police Officers (Acpo), said the current lack of access to details of internet communications was hampering investigations.
"There is a growing gap in our ability to maintain current capability," he said.
But Nick Pickles, director of the civil liberties campaign group Big Brother Watch, said: "If the government wants a serious review of spying laws then we will happily engage with that process.
"However, to rush out an announcement about local councils is neither a serious review nor a credible effort to protect civil liberties.
"It is a desperate attempt to buy off critics that says a great deal about how little support the Home Office believes there is for this policy."
He went on: "Making a complex area of legislation even more complex undermines accountability and will lead to even more abuses of surveillance laws.
"It is a naked attempt to avoid scrutiny and deliberately hide from the public details of the most intrusive surveillance regime of any democratic government."