Preliminary indications suggest the enquiry, ordered on Friday by the Minister of Commerce and Consumer Affairs David Clark, will have a limited scope..
It followed a storm of protest against the Act which came into effect in December.
Critics alleged that legitimate borrowers with a good credit record were no longer able to get access to the money they were previously eligible for.
This was because detailed expenditure such as takeaway food was being included in their monthly costs, sometimes leading to a credit downgrade.
In response to repeated criticism, Clark called for an inquiry by the Council of Financial Regulators (COFR) last Friday.
The COFR is an inter-departmental organisation made up of the Reserve Bank, Treasury, the Financial Markets Authority, the Ministry for Business Innovation and Employment (MBIE) and the Commerce Commission.
MBIE is the organising body for the Council.
It was due to hold its first meeting on Tuesday.
But comments from Clark suggested its scope would be limited.
“The COFR will convene to talk about the CCCFA which will trigger engagement with banks,” an official in Clark's office said.
“The Minister will be briefed in coming weeks.
“There are no terms of reference, (the inquiry) is less formal than that.”
These comments mesh in with earlier statements from Clark which were focussed on whether banks were properly administering the law rather than on the law itself.
This approach has been criticised by the brokers who want a more fundamental investigation.
A petition against the law in continuing.