The academies - independent state schools set up to raise standards in disadvantaged areas - refused to teach the children despite being named by the child's education authority as the school best able to meet their needs.
The revelation comes as research by Professor Stephen Gorard of York university suggests that academies are raising standards by improving their intake rather than doing better with the same pupils.
Professor Gorard's study of three early academies found that only one, Bexley business academy, is still serving the most disadvantaged pupils in the area.
Bexley academy was described as a "beacon of hope" by the Prime Minister but the Office for Standards in Education found it had "significant weaknesses", a finding disputed by the school.
Professor Gorard said: "There is no evidence that these schools are, in general, performing any better for equivalent students than the schools they replaced.
"There is nothing blameworthy in an academy with a disadvantaged intake moving over time towards the same composition as neighbouring schools.
However, it is hypocritical to then claim that the ensuing improved results in the school are due to the innovation, management or curriculum."
Academies have a duty to accept special needs pupils if they are named in their statement as the school most suitable for their needs. But local authorities do not have the power to name an academy without its consent, even if it is convinced that it is the best place for the child.
If the two sides fail to reach agreement the final decision rests with the Secretary of State, although parents can appeal to a special needs tribunal if they are unhappy.
In a letter to councils and academy heads, Jane Cook of the Department for Education and Skills academies policy unit, said: "There were a small number of cases last year where an academy and an LEA were not able to reach agreement together over the naming of an academy in a statement of special educational needs.
"Unfortunately some cases were not resolved by the end of the summer term, leaving some children without an agreed secondary school after leaving their primary."
The DfES is establishing a voluntary system of independent mediators to resolve disputes between academies and councils. Academies will also be offered independent advice on difficult cases.
A government spokeswoman said: "We are aware of delays in a small number of cases last year, but are confident that all cases were successfully resolved in time for the start of the autumn term and no child was left without a place."