Public bodies today indicated they would push to be given powers under a new law dubbed a “snooper's charter”.
Police and security services will be able to track suspects through their use of emails and websites in a bid to prevent problems catching criminals such as paedophiles and terrorists. But other authorities have not been named in the new legislation.
The UK Border Agency told MPs it needed powers under the Communications Data Bill to keep up with the technological advances enjoyed by criminals.
Gillian McGregor, UKBA director of operational intelligence, told a joint committee examining the proposals: "The serious criminals we deal with on the immigration and customs side are making increasing use of more sophisticated internet and smartphone techniques to communicate so I think it (the Bill) would potentially give us more options.
"We are looking to be able to retain the ability to keep up with the communications that the criminals we are dealing with are using.
"We understand that because technology is progressing the current information is perhaps not the whole story."
Under the reforms announced by Home Secretary Theresa May last month local authorities will not be able to track internet data and will also be stripped of their current powers to access information about phone calls.
But the LGA said today it had been advised by the Home Office that if councils wanted powers it would need to make a business case.
Cllr Paul Bettison, LGA regulatory champion, told the committee he was not seeking extra powers but wanted to retain those they already have.
"Not allowing local authorities these powers would leave councils without the necessary tools to protect their residents," he said.
He told MPs benefit fraud was difficult to prove and warned it was vital that councils were "seen to have the powers" to tackle crime.
The draft Bill does not introduce real-time monitoring or allow the content of communications to be subject to surveillance.
Ministers insists the reforms will enable law enforcement agencies to keep track with modern technology that is being exploited by criminals but critics claim the move compromises privacy.
Isabella Sankey, director of policy for civil rights organisation Liberty, said: "The Government's Snoopers' Charter will mean that billions of records of emails, phone calls and texts will be recorded for future monitoring.
"Unsurprisingly we now see local councils and other public bodies already pushing for access to the phone and web habits of the entire population.
"When the coalition came together they claimed to value our personal privacy - do they still mean it?"