Giving oral evidence to the education select committee's inquiry into the work of OFSTED yesterday, the LGA delegation said that LEA inspections were an important part of councils' drive to improve standards.
LGA education chair Graham Lane said: 'Local authorities are committed to raising school standards - that's why we support the role OFSTED plays in inspecting local education authorities.'
He added that independent inspection was vital if councils were to improve their services to the public.
LGA director of education Neil Fletcher, who also gave evidence to the committee, pointed out that the LGA was setting up a new body to concentrate on improving services.
He said: 'Our new Improvement and Development Agency will use good examples, like Newham and Bury, to spread best practice among other councils.
'Without the information we get from OFSTED inspections and other performance indicators, we could be condemning children to a second-class education. Once we know a service is failing, we can work with the authority to turn the situation around, just like we did successfully with Calderdale last year.'
On the subject of Chris Woodhead's sometimes controversial style, Mr Fletcher commented that although some authorities hadn't enjoyed the procedure, there were some who had found it rewarding.
He continued: 'Mr Woodhead's personal style is a just a side issue. What's important is OFSTED's work in discovering whether an authority or a school are doing a good job or not.'
The LGA also told the committee that more thought should be given to the appointment of the chief inspector. At the moment the local authorities, churches and other groups who are involved in education aren't consulted in the process.
After giving evidence, Ronnie Norman, the LGA's Tory education spokesman said: 'We think some kind of body might be appointed to support the chief inspector.
'I think this body should be made up of non-stakeholders to avoid any possible conflict on interest'.