The home secretary, Theresa May, has failed to win the backing of the Treasury to fund her £1.8bn "snooper's charter" programme to track everybody's internet and mobile phone use, ministers have revealed.

Danny Alexander, the Liberal Democrat chief secretary to the Treasury, has confirmed that the work on revising the business case behind the controversial project, including its cost and benefits, is already under way amid fears by MPs and peers that the final bill will only go one way – upwards.

Nick Clegg called for May to send her legislation underpinning the "snooper's charter" back to the drawing board after a parliamentary scrutiny committee warned that it "tramples on the privacy of British citizens" and amounted to overkill.

The draft communications data bill will require phone and internet companies to securely store every customer's data – social media, web and mobile phone use – for 12 months so the police and security services can use it to tackle serious crime.

The pre-legislative cross-party committee of peers and MPs, chaired by a former Tory Home Office minister, has described as "fanciful and misleading" the plan's estimated £1.8bn price tag over 10 years and claimed benefits of up to £6bn.

"The Home Office's cost estimates are not robust … The figure for estimated benefits is even less reliable than that for costs, and the estimated net benefit figure is fanciful and misleading," said their report. More than half the cost – £859m – is to cover the companies' costs.

In the first official response to the MPs and peers, Alexander has told the former Labour cabinet minister Nick Brown in a written parliamentary reply: "This expenditure is not yet committed, and so would represent an additional pressure were the report to go forward. The programme's business case is being revised at present, including the costs and benefits. The Home Office envisage completing this work by early 2013, and HM Treasury will consider the revised business case when it is available."

Brown, who sat on the scrutiny committee, said there had been little consultation with the industry on specific costs.

"Danny Alexander's answer confirms that there is no extra money for this. If it goes ahead it will be at the expense of existing police services," said Brown.

"The Home Office should think again and come forward with proposals that are more carefully targeted on the real issues and whose costs are more proportionate to the benefits. These pretty fundamental problems with the government's current proposals are in addition to the very real civil liberty objections."

One leading Conservative critic, David Davis, has described the costing as "written on the back of an MI6 fag packet" in reference to the Home Office architect of the plan, Charles Farr, who heads the office of security and counter-terrorism.

Before the scrutiny committee Farr strongly denied that there had been a lack of consultation over the costings with the phone and internet companies.

"We know in quite a high level of detail what those costs comprise and we have already formed the basis of our calculations about the costs that the communication service providers may incur in the future," he said during evidence. "We have added in considerable optimism bias on top of that. I would not want you to conclude that we plucked these figures out of thin air. They are based on existing costs which we have already established with the providers. It is still our view … that these figures accurately represent the likely cost going out to 2020."

He confirmed that the business case was to be "refreshed" but said he did not anticipate the exercise would come up with a figure higher than £1.8bn.

But the peers and MPs were not convinced. In their final report they quoted evidence from Steve Collins, the head of EU policy at Microsoft, that he was willing to bet that in 10 years' time the cost would have multiplied grotesquely.

"We think he would be betting on a certainty … Given successive governments' poor record in bringing IT projects in on budget, and the general lack of detail about how the powers under the bill will be used, there is a reasonable fear that this legislation will cost considerably more than the current estimates," they concluded.