The report also says LAAs and the third sector public services agenda have been developed "in parallel, by different parts of central government, with few, weak links between the two."
LAAs are contracts between councils and central government that are designed to devolve greater power over public services to a local level.
The report concludes that LAAs have so far failed to capitalise on the chance to improve links between charities and councils. "There is no evidence that they have increased public service delivery by the third sector, or that they will do so in the future," the report says.
Although the primary intention of LAAs was not about boosting public service delivery through third sector organisations, more must be done to improve their track record in this area, the report says. Councils should be more proactive in working with charities to improve public service delivery in their area.
The report included a survey of more than 70 charities. Sixty per cent of them said LAAs had no significant effect on the funding processes for the local charities and voluntary organisations.
It says relationships between councils and charities are often problematic. "Third sector organisations complain that they are excluded from contract opportunities, forced to accept below cost pricing and that their work is subjected to excessive monitoring," it says.
Councils often found charities and voluntary organisations in their area to be fragmented, the report says.
Joe Cavanagh, director of business development at the NAO, said the Government and local authorities must do more to understand the work of charities.
"Both main political parties have highlighted the third sector's important role in building a civil society," he said. "It is therefore disappointing that the new local area agreements have not embraced the potential of the third sector to help deliver public services."
To read the report, click here.