Levels of trust in councils have risen significantly over the last decade, according to the sector-led improvement baseline evaluation report by the Local Government Association.
Nearly two-thirds of residents trust their local council and 72% are satisfied with the way services are run, compared with just over a third of people expressing the same trust in Parliament.
The LGA said the report would give local councils confidence they were making the right decisions about driving improvement and service delivery while offering taxpayers value for money.
One of the coalition governemnt's early cost cutting measures was to abolish much of the regime of inspections and targets for local authorities, said the LGA.
This reduced the burden they placed on councils and saving in excess of £1 billion.
This has allowed councils the freedom to concentrate on finding new and better ways of measuring success, identifying areas for improvement and offering residents greater local accountability.
Three-quarters of council policy chiefs who were surveyed as part of the baseline evaluation believe that a sector-led approach is the right way to support improvement in the current climate.
Some 95% expressed confidence in their own authority's ability to deliver change.
In-depth independent interviews with senior civil servants and regulators conducted by Ipsos Mori as part of the report also showed strong support for sector-led improvement.
Peter Fleming, chairman of the LGA's improvement board, said said the old system of inspection and centrally-set targets was incredibly expensive to administer and out of touch.
"Considering 70 per cent of council spending is now raised locally, it simply wasn't achieving results," said Mr Fleming.
The sector-led approach to improvement was not a replacement for inspection. It offered a new way to ensure councils met local expectations.
"Ultimately we are answerable to our residents and the new approach to driving change is helping to improve services to meet local needs and offers transparency for both local and national audiences."
The baseline evaluation is the first of three reports to be published looking at the sector-led approach to improvement.
An interim review will be published towards the end of spring and final impact report in early 2014.
To access the full sector-led improvement baseline evaluation report, click here.