A proposal to allow Cheltenham listening post GCHQ to monitor any email, phone call or website visit of people in the UK has been condemned by internet firms.

The London Internet Exchange, which represents more than 330 companies, including BT, Virgin and Carphone Warehouse, says the Government's surveillance proposals are an "unwarranted" invasion of people's privacy.

The £2 billion project, pioneered by former Home Secretary Jacqui Smith, would allow the Benhall-based intelligence headquarters access to the records of internet providers in an effort to maintain its defences against terrorism.

The firms will be asked to collect and store vast amounts of data, including from social networking sites such as Facebook, although intelligence workers will not be able to view the actual content of emails and phone calls.

But the companies, who would have to co-operate with ministers for the scheme to be implemented, say the Government has misled the public about the extent to which it plans to monitor internet activity.

A private submission from the London Internet Exchange to the Home Office said: "We view the description of the Government's proposals as maintaining the capability as disingenuous – the volume of data the Government now proposes we should collect and retain will be unprecedented.

"This is a purely political description that serves only to win consent by hiding the extent of the proposed extension of powers for the state."

The criticism is the latest blow to the scheme. Ms Smith was forced to abandon plans for a giant database of internet records in April following privacy concerns.

She tried to salvage the project by announcing £2 billion of public money would instead be spent on helping internet providers to retain information for up to 12 months.

But the London Internet Exchange said the proposals were unworkable.

It said: "We aren't aware of any existing equipment (an internet firm) could purchase that would enable it to acquire and retain such a wide range of data.

"In some common cases it would be impossible in principle to obtain the information sought.

A spokesman for GCHQ said: "The Home Office has consulted publicly on its proposals.

"It recognises that this is a complex and sensitive subject with a fine balance to be made between protecting public safety and civil liberties.

"GCHQ is providing technical advice and support to the Home Office and has no plans to monitor all internet use and phone calls in Britain."