Academy sponsors and other organisations could be allowed to retain control over state schools even if their performance is judged so poor that they lose their Government-approved kitemark.
Ministers are setting up an Accredited School Providers scheme to ensure that external organisations running state-funded schools are suitable and held accountable for their performance.
But a document setting out the detail of the scheme shows that the providers could continue to run schools even if they have been stripped of their accreditation.
John Bangs, NUT head of education, said: "This looks as though the DCSF wants to retain the political whip hand over whether or not to offend a sponsor, and that is totally arbitrary. There is no consistency at all."
It emerged as local education officers warned that the criteria needed to gain the kitemark were too loose and did not specify the kind of expertise necessary to turn round poorly performing schools.
And it comes amid government concerns about the performance of its biggest academy sponsor, United Learning Trust.
The kitemark scheme is being set up to cover the increasing number of educational institutions, charities and private companies running academies and other, often under-performing, state-funded schools through trusts and federations.
The introduction to the scheme by Ed Balls, Schools Secretary, reads: "For these formal partnerships to succeed, we know that the lead partner or sponsor must be accountable for the improvement in the school it is supporting and have the track record, capacity, educational expertise and school improvement experience to secure rapid, sustainable improvement."
To gain accreditation, he says, they must demonstrate sound governance; effective leadership and management; a strong vision for managing and improving schools; a track record of improving pupil outcomes and the capacity to achieve transformational change in the schools they are supporting.
But they can also lose it if their performance drops, there is no improvement in the performance of a school they are supporting, the performance of the school drops, or the organisation breaks the law. In the latter circumstances, the loss of accreditation will automatically mean the organisation loses control of its schools.
But in all other cases where the kitemark is withdrawn there will be no automatic removal of schools, a government consultation document reveals.
Instead, the local authority - or if the school is an academy, the Government - will decide their fate on a case-by-case basis according to whether "it is judged that the lead provider has had no positive impact on the school".
Aspect, the union representing local education officers, argues that the criteria being set for providers need tightening up.
It says that when assessing organisations' educational track records there is a lot of emphasis on outcomes, but not enough on how they were achieved.
It also points to a focus on academic standards, with very little on the wider aims of Every Child Matters.
John Chowcat, general secretary, said: "The criteria are too soft and too loose. They should be giving confidence to every school in the country that if they under-perform they will be supported by skilled professionals with specialised expertise in school improvement."