A letter signed by chairs of governors of the three, which will shut in September 2007 to make way for the pound;46.5 million Thomas Deacon academy, said there had been a culture of secrecy surrounding the plans.
They said there had been a "disregard of and disinterest in" the predecessor schools and the local council by the sponsors. They said they had only received three newsletters in 15 months updating them about the plans.
They also raised doubts whether the principal sponsor, Perkins Engines, which produces industrial engines, has enough "detailed educational expertise" needed to lead the school. "The expertise involved in what is to be an exclusively people-related organisation contrasts significantly with a manufacturing environment," says the letter signed by governors from John Mansfield school, Deacon's school and Hereward community college.
However, a spokesman for Perkins rejected the claims, pointing out that the Deacon's Trust, an educational trust set up in 1722, is part-sponsoring the school.
"We are not running the school, we are merely ensuring that the right people are put in place to run it," he said, adding that the firm was "very surprised" by this letter - and was already dealing with many of the issues it had raised.
Meanwhile, another academy due to open in the heart of London in September has been dealt a blow after its sponsor pulled out.
The Westminster academy, being built near Paddington station, will go ahead as planned even though Chelsfield, a property company, has yet to pay the full pound;2m sponsorship.
Chelsfield, which has played a major part in a massive canalside development behind the station, had been heavily involved in local regeneration projects, including the local education action zone. But 18 months ago it was bought by a consortium including Multiplex, the Australian-owned company building the new Wembley stadium, which has decided not to proceed with the project.
The trust that Chelsfield set up to develop and run the academy will continue to oversee its development as the Government searches for another sponsor.
An MP has criticised Westminster academy over plans to charge parents up to pound;90 for a new uniform. A one-off subsidy from the Government will bring that down to pound;30 for pupils transferring from the comprehensive it will replace - but parents of children moving from primaries will have to pay the full pound;90.
Karen Buck, the local Labour MP, said: "For those with two or three children transferring to the school it will be an enormous financial burden."