In their formal response to the final proposals, produced in November, the associations focus on the main anomaly which would see councils which have embraced partnership with the private sector being forced to expose more work.
'No-one dreamed that anyone could make the bureaucratic nightmare of CCT even worse, but the government is managing to achieve just that,' said Neil Turner, chair of the Association of Metropolitan Authorities public services committee.
'There is particular concern about the impact on personnel and financial services. Many authorities have already contracted out those parts of these services which make clearly identified packages for tendering purposes,' said Mr Turner.
Westminster City Council and Bromley LBC, which have embraced the competition ethic, have both pointed out that the new regime would hit them harder than other councils.
Other areas which have been heavily criticised include not allowing credit for DSO work in meeting the competition requirement, the short consultation period and the proposed implementation timetable.
The DoE this week said that it had received around 200 responses to the consultation - despite attempts to limit the consultation to 20 representative bodies.
The proposals have been criticised by the private sector. The Royal Institution of Chartered Surveyors expressed concern that the debate about the detail of the regime is distracting from the need for councils to obtain best value for money.
In their response to the proposals competition experts Stephen Cirell and John Bennett of Eversheds say there are four simple amendments which could be made to make the changes fairer.