The National Union of Teachers (NUT) is urging the government to scrap its plans for free schools and "stop playing with the educational future of this country".
Christine Blower, the union's general secretary, said the schools are "not wanted or needed".
A YouGov survey commissioned by the NUT found that 31 per cent of parents are opposed to them, while 26 per cent are in favour of them and 29 per cent are undecided.
"This survey clearly shows that parents are not clamouring to set up free schools, have no issue with schools being accountable to the community through democratically elected local authorities and absolutely reject the premise of their children's education being handed over to private companies," Ms Blower commented.
A spokesperson for the Department for Education said it is disappointing to see the NUT continuing to "blindly oppose" free schools before one has even opened its doors.