Just a quarter of parents support the creation of a free school in their area, according to figures released this week.
A study carried out by YouGov for teaching union the NUT, showed that of 1,021 parents questioned in 22 local authorities, only 26 per cent backed the introduction of a free school in their neighbourhood.
The new-style schools, the first of which is expected to open in September, form a major part of prime minister David Cameron's "big society", giving parents, teachers or charities the power to open a new school if they are not happy with existing provision.
NUT general secretary Christine Blower said the figures showed free schools are "not wanted or needed".
"They are divisive and unaccountable," she said. "The teaching profession and parents know this. It is time the Government stopped playing with the educational future of this country based on nothing more than the fact they can."
The Department for Education said it was "disappointed" to see the NUT "continuing to blindly oppose" free schools before one has opened its doors.
A DfE spokesperson said: "It is also parents themselves who are behind many of the free-school proposals - parents who want something better for their children. And even where parents are not the lead proposer, each proposal has to show there is demand locally for the type of education they plan to offer."