The system, which looks for matches between a council's payroll and benefit claims, has already been run by Sheffield City Council, throwing up 1,280 suspects out of a total workforce of 30,000.
Other councils are expected to follow suit and request their district auditor to run checks.
The move has prompted an angry response from Unison. The Sheffield branch accused the council of scapegoating workers on low wages.
The Audit Commission is now promoting the system through nationwide seminars and is urging other councils to run checks. But district auditors have to be invited by councils to match records.
Sheffield says of the 1,280 names produced by the search only 28 merited investigation. Nine have been scrutinised, with six cases referred to senior officers for action.
One person has already been dismissed for gross misconduct.
A spokesman for the council said it was asked by its district auditor, Gordon Sutton, to run the computer check, and denied there was a witchhunt of low-paid staff.
'Everyone in the organisation from the chief executive downwards was checked,' he said.
He added that there was no evidence that Sheffield had a higher level of fraud than any other council.
Brendan Wood, chief executive of Unison's local government branch in Sheffield, said the district auditor's time would be better spent tackling fraud by landlords.
The commission's regional computer auditor for London, Peter Yatzes, who helped develop the system, said investigations in the rest of the country were unlikely to reveal the same volume of fraud uncovered in London.
Fraud in London is higher because there is greater opportunity for multiple claims at several councils, he said.
But Mr Yatzes warned against complacency, saying there was also evidence of fraud in shire county areas.