Adair Turner, director-general of the Confederation of British Industry, said awareness of the date change problem had increased dramatically, but warned there was a "dangerous reluctance" among firms to convert that concern into action to solve the problem.
"While there are 732 days still to go to the Millennium, the final year must be used for preparation and testing. Firms need to use next year to ensure they are compliant," he said.
"The Millennium date change affects every company in the country and while many appear now to be aware of it they seem reluctant to take action. This must change - if firms want not only to retain their business partnerships but to stay in business, they must act and act fast."
The root of the problem is that many computer systems which record the year with two digits may be confused at midnight on 31 December 1999 when "99" is replaced by "00". The systems will fail or data errors will appear unless they have been reprogrammed to avoid computers mistakenly registering the year 2000 as 1900 instead - a problem which could result in meltdown.
The "Millennium timebomb" could affect almost every aspect of daily life, including using credit cards, the payment of wages and salaries and the provision of health service in hospitals.
It is estimated the cost of dealing with the problem could be pounds 30bn and a survey by PA Consulting found that almost half of a sample of businesses did not have a formal plan of action.
The Government has earmarked almost pounds 400m to defuse the problem within Whitehall in the face of criticism ministers were not doing enough to prevent the problem affecting the Civil Service.