New Free Schools, set up less than a year ago and free from local authority control, are hugely over-subscribed, according to Government figures.
Twenty-two of the 24 Free Schools which opened last September responded to a Department for Education (DfE) survey, with 19 reporting being over-subscribed for the coming school year starting this September.
On average, primary Free Schools attracted more than twice as many applications for the number of places available.
The secondary, or all-through, Free Schools, on average received well over three times as many applications for the places available.
Free Schools are being set up by teachers, parents and charities where there is parental demand and, in the main, in areas of deprivation.
Schools Minister Lord Hill said the figures underlined the popularity of Free Schools with parents.
"These figures show how keen parents are to send their children to Free Schools," he said.
"They provide the answer to the naysayers who said that Free Schools weren't wanted or needed - or that no one would be bothered to set them up.
"They are also providing a spur to other local schools to do the best they can."
* 554 parents applied for 132 places in Batley Grammar School's primary and secondary phases. The school, in Yorkshire, has the largest waiting list in Kirklees.
* 1,078 parents applied for the 120 places at West London Free School in Hammersmith. More than 250 parents put the school down as their first choice.
* 704 parents applied for 160 places on offer at Kings Science Academy, in Bradford.
* 80 parents applied for 24 places in the Free School Norwich's reception class. Eighteen children are waiting for places to become available in each of the other classes in the school, which is now considering a new building to cope with demand.
Tania Sidney-Roberts, principal of Free School Norwich, said: "The Free School Norwich is three-and-a-half times over-subscribed again for this September and we are currently operating waiting lists of at least 18 children in all year groups across the school.
"This demonstrates just how desperately needed the service our school provides is.
"A recent parent feedback survey carried out by the school also indicates that 100% of our parents are very happy with the service and that their children love coming to the school and are making excellent progress.
"I am obviously delighted to have confirmed in this way what we always knew was the case - that the freedom given to Free Schools to be innovative and to meet the needs and preferences of parents was long overdue and it works."
Dr Brinder Singh Mahon, chairman of the Nishkam School Trust, in Birmingham, added: "We have been very disappointed to turn away over 50 families who could not be accommodated in the school."
Malcolm Trobe, deputy general secretary of the Association of School and College Leaders, said he had concerns about pupils at other schools missing out on funding.
He said: "It's perfectly understandable that parents want to send their children to schools that have had investment in new facilities, and can afford small class sizes and extras like free iPads, rather than the good school down the road which may have a leaking roof and crumbling buildings.
"Where there is a shortage of places, opening a new school makes sense.
"The problem is opening a new school where there is no real need.
"Our concern is for pupils who remain in good and outstanding schools down the road from a new Free School, who are losing out in terms of funding and resources."