A draft prospectus for potential sponsors of the new schools - an attempt to rescue the ailing Fresh Start policy - beefs up the role of education authorities and plays down the demands on investors.
Sponsors will now be asked to contribute "up to around 20 per cent" of building costs for the school, in cash or in kind. Earlier versions talked of contributions of "around 20 per cent" and made no mention of alternatives to cash.
John Bangs, head of education at the National Union of Teachers, said: "The Government has been forced to confront the reality that private companies aren't interested in investing in schools. They should have learned that from education action zones.
"This is a massive climbdown but it still needs to grapple with their failing Fresh Stat policy."
The academies would be sponsored by business, religious groups or the voluntary sector and would usually replace one or more failing schools. They would be independent schools operating in the state sector but outside the local authority framework.
The Catholic education service is due to discuss the proposals later this month, but the Church of England has rejected approaches.
The revised prospectus encourages sponsors to invite the local authority onto the governing body and envisages that "sponsors will normally work with LEAs to identify situations where city academies represent a positive way of tackling underachievement".
Any proposals to close a school to make way for a city academy would be expected to come from the LEA - making their involvement almost inevitable.
The changes were welcomed by the Society of Education Officers which said they would ensure the academies became part of the local family of schools.