The country's biggest academy sponsor is suffering a backlash from teachers and parents after the Government agreed that it can continue with planned schools despite concerns over its performance.
Ministers have stopped United Learning Trust (ULT), which currently sponsors 17 academies, from further projects until it improves standards in its existing schools.
But the Christian charity is allowed to carry on with plans for two schools to replace Oxford School and Weston Favell School, Northampton, in September next year.
Teaching unions and parents at the schools are now urging their local authorities to revisit their decision to use ULT.
Lyn Cooper, NASUWT executive member covering Northamptonshire, said: "We were aware that a number of their academies were not doing well. But now that the Government has acknowledged problems, we want the council to reconsider its decision."
Vernon Coaker, the schools minister, wrote to both Oxfordshire and Northamptonshire councils earlier this month about their academy plans.
Mr Coaker praised ULT for being "bold and courageous in taking on some of the most challenging predecessor schools in the country".
But he also acknowledged its problems. "While there are encouraging signs, equally clearly, there is still some way to go before all ULT's academies are making the consistent progress towards transformational change that is the goal and expectation of the academies programme," Mr Coaker wrote.
He added: "In view of the challenges it faces, and which it acknowledges, we have asked ULT to continue to focus in particular now on its existing academies whilst developing its two new projects."
ULT came in for criticism after two of its academies in Sheffield were described as inadequate by Ofsted this year. In September, one of them, Sheffield Park, became only the third academy to be placed in special measures.
Concerns have also been raised about the high turnover of headteachers at ULT schools, with more than half of its principals leaving within two years of schools opening.
Anna Thorne, whose twin sons attend Oxford School, said: "I am very concerned. I don't see why our school should end up with a sponsor that is not considered to be sufficiently capable by the Government.
"However they put it, at the end of the day they are saying that ULT is overstretched and need to make improvements in the schools they are already managing."
Ms Thorne, who has written to the Government and local authority, is against the academy plans irrespective of the sponsor.
Oxford School's provisional contextual value-added score this year is higher than any other school in the county achieved in 2008, she said.
Brenda Williams, secretary of the Oxfordshire NUT, said: "I don't think we should have an academy full stop, but now it appears to be going ahead even though ULT can't have any more schools in other places."
Parents of pupils at Weston Favell voted strongly against plans to turn the school into an academy when governors carried out a survey earlier this year.
Oxfordshire and Northamptonshire councils said they were both pushing ahead with their academy plans, with ULT as sponsor.
An Oxfordshire County Council spokesman said: "ULT already sponsors the North Oxfordshire Academy and the council's experience of working with the organisation has been positive."