More than half of the free schools that opened last year did so with spare places, having failed to recruit as many pupils as they had been aiming for, new Department for Education (DfE) figures have revealed.

Nearly six out of 10 of the government's flagship free schools opening in 2012 did so at only 90% of their stated first-year capacity or less; while 10 schools – nearly one in four of the 44 mainstream free schools for which full data is available – opened at 60% or less of the student numbers predicted.

Two comprehensives had only 40 pupils on their books; one school for 14- to 19-year-olds also had only 40 pupils; while another secondary free school had recruited only 35 students. On average, free schools opening in September 2012 – the latest for which there is official data – did so with 16% fewer pupils than they were predicting before opening.

The news will intensify the controversy over free schools, with critics questioning whether they represent an efficient use of resources. The National Audit Office this week highlighted the rising costs of the free school scheme, with £6.6m on average allocated to each school for building costs. The NAO said: "The primary factor in decision-making has been opening schools at pace, rather than maximizing value for money."

The Guardian analysis combines the latest school census data with official DfE predictions of free school pupil numbers and school funding information.

DfE school census data, collected in January 2013, was compared against the official total capacity of free schools that opened in 2012. It was also compared against the 2012-13 enrolment numbers predicted for the schools, as revealed in separate DfE "impact assessment" documents on each institution, which were used to assess their potential impact on rival local schools before they were set up.

The data reveals that, as of this year, most free schools that opened in 2012 were operating at well under their long-term capacity. This is in part to be expected, as most schools recruited only one or two year groups on opening, with the plan of reaching capacity in several years' time. However, many under-recruited even within those year groups where they did admit pupils.

Of the 44 mainstream free schools to have opened in 2012, 26 were operating with more than 10% spare places as of January 2013, compared with the recruitment numbers predicted for them for 2012-13 in the school's impact assessment before opening.

At Sandymoor free school, a comprehensive for 11- to 18-year-olds in Runcorn, Merseyside, the census records the school as having only 40 pupils in January 2013, compared with a prediction in its impact assessment of 80 and an eventual capacity of 900. The school lists 12 staff on its website for 2013-14. Sandymoor is receiving £1m from the DfE to cover the extra cost of building up pupil numbers over time, separate government funding data reveals.

Andrew Green-Howard, the school's head, said the school's capacity had been reduced in its first year to 45 by its local authority to cut traffic congestion. But total pupil capacity for its second year was running at 120, of which 105 places had been filled.

He said: "Our current numbers coincide with the lowest predicted years of population growth, before we get a population bulge, with 1,200 homes being built nearby. A group of five parents set up this school because there was no small secondary in the area, and there is demand."

At Atherton community school in Atherton, Wigan, 40 pupils were on the books in January, compared with a prediction for 2012-13 of 90. The school, which has a "Christian ethos" though is open to all, has capacity for 650 pupils eventually. Some 27 staff are listed on its website. The school is receiving £996,000 to build up capacity from the DfE. Atherton replaced a school that was closed by the local authority in 2011. In 2009, Wigan council said the pupil intake of 93 for the predecessor school that year made it unsustainable.

Russell Rook, chief executive of Chapel St, a charity sponsoring the new school, said it now had 103 pupils across two year groups, compared with a capacity of 180, but had received more applications than places for its next intake of year 7 pupils in September. He added: "Atherton is a town of 24,000 people which otherwise would not have a high school – 97% of local people said they wanted a school within walking distance of their home, and that is what we are providing."

Wapping high school, an 11-16 comprehensive in Tower Hamlets, east London, had only 35 pupils on its books in January, compared with a prediction of 81. The school's website says it did fill all 84 available places for 2013-14 this September.

Saxmundham free school, in Suffolk, had 110 pupils in January, barely half of the 216 predicted in its impact assessment. The school's website currently lists 34 staff. It and Beccles free school, another free school in Suffolk that was undersubscribed in January and is part of the same group, are together receiving £1.64m as they build up pupil numbers.

Rob Cawley, principal of the Seckford Foundation free schools trust, which runs both schools, said the school still only had 171 pupils but there was "a clear parental demand … for something different, and the free schools movement is about more than just school places. It is also … about creating competition in the education system to raise standards."

Rimon Jewish primary school, in Barnet, north London, opened with just 15 pupils in 2012, against an official prediction of 28. This means that, in its first academic year, the school was operating at just 8% of its long-term capacity of 196 pupils. It is receiving £570,000 to build up numbers.

And Harpenden free school, a primary in Hertfordshire, had only 35 pupils in January 2013, against a prediction of 60. John Gibson, its headteacher and chief operating officer, said the school had filled all 60 places for 2012-13 by the end of the last academic year. It currently had 98 children.

The Rural Enterprise academy, a free school in Penkridge, Staffordshire, focusing on rural, environmental and sustainability education, had 40 students on its books in January, only a third of the 120 pupils predicted in its impact assessment, although a spokesman for the school said the initial capacity figure had been revised down by the DfE. The academy now had 84 pupils, he added.

Several non-mainstream, "alternative provision" free schools – institutions largely set up to educate pupils who have been excluded from other schools – also registered only handfuls of students on the census date of 17 January. Three schools had only five pupils each at this time. One of them, Derby Pride academy, was set up after the DfE spent £2.15m on land and buildings costs.

The free schools opening in 2012 are the latest for which official school census data, collected in January each year, is available to enable admittance patterns to be checked. The first batch of 24 free schools, which opened in 2011, seem generally to be operating at or near capacity for the year groups admitted. A further 93 free schools opened in September 2013.

John Fowler, policy manager for the Local Government Information Unit, whose initial analysis of the figures prompted the Guardian's investigation, said: "A significant number of free schools opening in 2012 seem to have under-recruited. Questions need to be asked about why any of these schools are opening at, say, 40% under capacity in individual year groups."

A DfE spokeswoman said: "It is perfectly normal for any type of new school to take time to fully establish itself. The vast majority of free schools that opened in 2011 are now more than 95% full, with many oversubscribed. There is nothing to suggest that the 2012 openers will not follow a similar pattern."