Cookies are used to provide visitor details to site administrators, often so that each surfer can be presented with the most relevant information.
Under the new law, visitors to websites must be given "clear and comprehensive" information on how the information will be collected and used. Users will also have the right to object.
But Alex Chapman, of law firm Briffa, insisted that the figures are unsurprising - and that many firms need clarification of the law.
"I am not surprised that 98 per cent don't comply. I would be surprised if even two per cent did comply," he said.
"This law, which has good points, is another example of laws made by people who don't really understand the internet.
"Guidance from the Department of Trade and Industry and the Information Commission is unclear.
"What happens if someone objects? Will they have to be directed to a mirror site with no cookies? At the very least they must be given help on how to disable cookies."
Policing the situation might prove a problem for the agency responsible, the Information Commission, which declined to comment other than to disagree with WebAbacus' figures.
"We don't know what criteria [WebAbacus] has used, so it is difficult for us to comment. But their figures don't match mine," said Faye Spencer, a complaints manager at the Commission.
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