Commission controller Andrew Foster made the threat after publishing a report showing councils - particularly districts - have slipped further behind the NHS and emergency services.
The report, Time marches on, says: 'The situation in local government is becoming more polarised, with district councils as a group falling further behind.'
During the six months to September, districts generally made just a quarter of the progress made by NHS bodies towards a set of Audit Commission benchmarks.
Unitary and metropolitan authorities made the most progress, closely followed by counties. However, all three groups fell further behind the NHS and emergency services.
The report urges public sector bodies to prepare contingency plans by the middle of next year. Four in 10 councils - double the proportion of NHS bodies - had not begun preparing such work when the audit teams visited them.
The Local Government Association said: 'We are serious about tackling the millennium bug. The report does recognise the progress that some authorities have made and obviously others need to make progress.'
Time marches on, is available from the Audit Commission, tel: 0800 502030.