A quarter of the free schools which opened in England this year are significantly under subscribed, figures obtained by the BBC suggest.
Fifty five new schools opened this September, bringing the total to 79.
Free schools are semi-independent state schools set up and run by parents, teachers and charities.
Education minister Lord Hill said there were a number of reasons that schools might not be full in their first year.
The BBC contacted all of the 55 free schools which opened this September. They were asked for the total number of places they were seeking to fill and how many pupils they had recruited.
Of these, 41 replied with their figures.
The data showed 14 had significant spare capacity, many with either a half or a third of their places unfilled.
They include Avanti House School in Harrow, the largest free school in England. It has places for 240 children but recruited only 130 pupils.
Wapping High School in east London was less than half full, with 38 pupils but places for 84.
The Al Madinah Muslim School in Derby fared better with 240 places filled out of a possible 300.
Supporters of free schools believe the small numbers in some schools have been caused by them securing their funding in the spring and summer long after most students had already made their choices.
One of the most contentious projects has been the Beccles Free School in Suffolk, which campaigners had tried to prevent opening. It has 87 pupils but places for 162.
Jeremy Rowe, head teacher of the existing Sir John Lehman Secondary School in Beccles, said the figures show they did not need another school in the town.
"It's a fact there is not the demand. There are thousands of spare school places in Suffolk and no local school is full. Is there the money for it? That seems incredible to me."
The Seckford Foundation charitable trust runs the Beccles Free School and another in Saxmundham.
This too had large numbers of spare places with 106 pupils but capacity for double that number.
The trust's director, Graham Watson, said free schools could not be judged so early on,
"Let's take the longer view, this is about education for the next 30 or 40 years, it's not the next 30 weeks "
The National Union of Teachers has made several freedom of information requests for reports and data used by the government when determining which free schools to approve.
NUT deputy general secretary, Kevin Courtney, said most parents wanted education to remain a public service and not to be hived off.
"We don't think there's any pent up sense of huge parental demand for free schools," he said.
Rachel Wolf, director of the New Schools Network which advises free schools, said finding a suitable site can cause delays and deter parents.
'Problem of scale'
"It is sites that is causing the problem more than anything else. You have to remember that this is a problem of scale, the DfE used to have to deal with a few schools a year now they are dealing with hundreds a year."
A spokesman for the Department for Education said: "Most new free schools are starting with one year group. That means numbers will grow quickly in years to come.
"The first free schools, which opened in September 2011, were all over-subscribed this year. We expect pupil recruitment for free schools opened in 2012 to increase steadily."
Lord Hill, the education minister responsible for free schools, said there were a number of specific reasons some schools may not be full but did not give any further details.
He said he was confident that would change.
"It's clearly the case that I want these schools to be successful and full and to be popular with parents."
He added: "We have the view that even in area where there's a surplus of places we still think parents should have the opportunity of a choice of a different kind of school even though that will obviously introduce a greater element of competition into the system."