The move followed the publication last week by the union of a report, Free Schools – Free for All?, in which it calls for the programme to end and for existing free schools to be brought under the mainstream state education system.
The report also wants to see local authorities given back control over school admissions.
The union said that warnings issued by the Liberal Democrats three years ago over free schools had now become reality.
At its conference in 2010, the party expressed concern over the government’s flagship policy and stated that local authorities should have strategic oversight of school place provision. It warned of the creation of “surplus places ... prejudicial to the efficient use of resources in an age of austerity”.
In its report, the union said that local need should be a “determining factor” in any decision to open a new school, and that “the interests of children will be best served by a return to a system of co-ordinated school place planning, carried out by local authorities with restored powers to plan and provide new school places where need is identified”.
Christine Blower, the NUT’s general secretary, said: “The Liberal Democrats’ warnings went unheeded by the government. We now face a schools places crisis as the government wastes scarce resources on establishing free schools in areas that have a surplus of places.
“The NUT’s report highlights how the Liberal Democrats’ fears of 2010 are fast becoming a reality in 2013.”
Ms Blower said that the deputy prime minister needed to “grasp the nettle of the school places crisis that is happening on his watch and put a halt to the wasteful and unnecessary free schools programme”.
However, at the Liberal Democrats annual conference last week, Mr Clegg used his speech to launch a free school meals drive for infant pupils.
In July, the DfE blamed the previous administration for not reacting to rising birth rates, arguing that the coalition has more than doubled funding for new school places.
The DfE said that while the government allocated £1.9 billion to creating new places between 2007 and 2011, the coalition has allocated £5 billion between 2011 and 2015.