From 25 May, firms will have to have the explicit consent of customers in order to store any cookies. The law is being introduced by the European Commission as part of an amendment to the Privacy and Electronic Communications Directive.
Information commissioner Christopher Graham said that firms needed to make sure they were ready for the change and that, while it might cause some short-time upheaval, it would have long-term benefits.
"The Directive will come into force in less than two months' time and businesses and organisations running web sites in the UK must wake up to the fact that this is happening," he said.
"While the rollout of this new law will be a challenge, it will have positive benefits as it will give people more choice and control over what information businesses and other organisations can store and access from consumers' own computers."
Graham added that the ICO, government and businesses are discussing ways in which changes could be made as simply as possible, including the possible use of setting cookie approvals through browser settings.
However, while the ICO is alerting businesses to this change, the Department for Media, Culture and Sport, which is charged with handling such matters, has said that the watchdog will go easy on firms that are slow to implement the necessary systems.
"We recognise that work will not be complete by the implementation deadline. The government is clear that it will take time for meaningful solutions to be developed, evaluated and rolled out," said communications minister Ed Vaizey.
Graham's comments were made at the ICO's annual Data Protection Officer Conference in Manchester on Tuesday.
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