Perry Beeches governors 'would be removed' under council
Governors at the Perry Beeches chain of academies and free schools would have been removed if they had been under Birmingham City Council control.
Councillor Brigid Jones, member for children's services, also said the head would almost certainly have been suspended.
A government report recently highlighted that the trust paid its chief executive a second salary.
The DfE said it is satisfied the trust is responding positively to concerns.
The Education Funding Agency Investigation found that trust's chief executive, Liam Nolan, was paid an additional salary through a supply company.
The payments, at least £160,000 over two years, were not disclosed in financial statements, the report said and were on top of Mr Nolan's salary of £120,000 per year for his executive head teacher role.
Mr Nolan has since stepped down as CEO but remains as executive headteacher of the five schools which look after 2,400 pupils.
The trust, which runs five secondary schools in Birmingham, has been praised by the government in the past with David Cameron and then education minister Michael Grove attending the opening of Perry Beeches III in 2013.
An Ofsted report in June 2015 said it should go into special measures. The headteacher and governors resigned.
Ms Jones said if the school had been under city council control, governors would have been replaced with an executive board of expert governors and the head and anyone else implicated would almost certainly have been suspended.
"Perry Beeches answers directly to the government, so I think they should take this as seriously as we would have taken it, replace the governors, and get to work putting the schools right."
The DfE said:"We are currently working with Perry Beeches to ensure it addresses concerns raised and this remains our priority.