Renewing democracy, rebuilding communities, published last week, made a commitment to replace CCT with a Standards Inspectorate and the requirement that all councils publish local performance programmes, saying what people can expect in terms of the quality and cost of service delivery.
However, the party has so far refused to say exactly when it will remove the compulsion on authorities to put contracts out to tender if it gains power at the next general election.
The associations are examining the legislation for ways in which compulsion could be removed without resorting to a further bout of time-consuming primary legislation.
So although it would not be possible to quickly abolish the 1988 act which introduced CCT for most manual services, it would be very easy to eliminate those services - such as leisure management and other white-collar services - which have been added by means of secondary legislation.
In addition, Labour would be able to allow councils greater flexibility in how they deal with the trade-off between quality and cost, so they were not forced to take the lowest bid every time.
In a separate development, Labour has begun a project to develop ideas for local performance programmes. Ten pilot councils, including Kirklees MBC, Ipswich BC, North East Lincolnshire UA and Birmingham City Council, have been selected to pioneer this idea.
'We are looking for councils to try different approaches to putting this idea into practice,' said Abigail Melville, Labour's assistant local government officer.