The council, which has recently reversed an earlier decision to close the boys' secondary, is opposed to being forced to hand over control of the school to external experts. However, the governors are willing to co-operate with an educational association as a means of securing the future of the school.
According to Tony Burgess, chair of governors and a reader in education at the Institute of Education at London University, governors are worried about the council's commitment to keeping the school open.
The council's decision to keep the school open was taken against the advice of the director of education, Gus John, and was made after a change in the political balance of the council. The former chair of Hackney Downs, Pat Corrigan, who had supported closure, lost his position as chair of education.
The new chair, Mr Burgess, says he is confident councillors are committed to the school, but governors fear that support within the education directorate is lukewarm.
"There is gap between the views of councillors and that of the officials. There is a view that Mr John wants the school closed," he says.
The governors were due to discuss their response to Mrs Shephard's letter - in which she says she is minded to send in an educational association - on Thursday.
"We will listen to what the council has to say about the kind of support that will be provided. An educational association does represent a possible way forward and we would co-operate with whatever authority was imposed," says Mr Burgess.
The governors blame the council for the fall in numbers to 250. The school has been unable to recruit pupils for September because of the original decision to close the school in July.
Mr Burgess believes the management of the school has improved. The school was judged to be failing last summer by the Office for Standards in Education which identified high levels of truancy, poor achievement and discipline problems.
In her letter, Mrs Shephard makes clear her view that the decision to keep Hackney Downs open has further weakened the school and that she is concerned that the local authority and governors may not be able to implement their action plan effectively.
However, Hackney council is adamant that an educational association is not required. The chair of education, David Phillips, says: "The Government's threat to intervene is untimely and unwise. The school is showing signs of improvement."
There are now more than 70 failing schools, but Mrs Shephard has yet to use her powers to send in an educational association. The association would replace the governing body. Its role would be to turn round the school and it would then opt out. Mrs Shephard retains the option to close the school if it does not improve standards of achievement.