In some areas of England, more than 1,000 children are not getting their preferred option.
It comes as education lawyers warned that the number of parents appealing against their school allocation is rising rapidly.
A survey of 42 out of 150 local authorities in England, conducted by the Press Association, reveals that, according to the latest figures available, more 16,800 children have not got a reception class place at their preferred school.
In Birmingham and Kent more than 1,600 have not been a allocated a place at their first choice, and in Hampshire that figure was more than 1,200.
These are among the biggest local authorities, and have larger numbers of children.
Councillor David Kirk, Hampshire County Council's executive lead member for education said: "The proportion of parents offered their first or second preference of primary school in Hampshire compares favourably with other authorities.
"The reasons why parents don't get their first preferred school varies for each case. However, the authority ensures that every child in Hampshire is allocated a school place."
Later this week, the Government will publish new data showing how many parents are appealing, against both primary and secondary school decisions.
The figures are likely to show a rise, particularly because parents who may have considered private education are now choosing the state system as they feel the effects of the recession.
Government figures published in March showed that almost 92,000 11-year-olds failed to gain a place at their first choice of secondary school this year.
Ian Jones, of school-appeal.org.uk, said: "There's been an enormous increase in my work on school appeals this year.
"It's partly due to the rise in availability of information about schools and the records you can get - you can get Ofsted reports at the touch of a button."
He added: "There has also been a rise in the number of people who appeal because of their own circumstances. They're not going into private education, they are having to stay put in an area."
These parents still want to ensure their child gets into the school they choose, and are willing to appeal if necessary, he said.
"Parents are not afraid to fight for what they want," Mr Jones added.
Jeremy Haw of schoolappeals.com said they have doubled the number of associates they have working on appeals this year, to cope with demand.
He said: "People at the margins on private education, who would often take out a loan against their property so they can pay the fees, can't do that now."
Mr Haw said part of the problem parents face with primary school admissions is the legal limit of 30 pupils per class.
This means that pupils can miss out if schools are heavily over-subscribed.
He said parents were increasingly seeking legal help to appeal this, but they need a strong reason in order to get it overturned.
"What you do find is that the chance of winning a class size appeal varies among local authorities. Some stick to it rigorously, others are somewhat lax," he said.
A spokesman for the Department for Children, Schools and Families said: "Allocating places fairly and equally is genuinely difficult. Quite rightly, it is for local authorities and schools, not ministers, to do this, in line with the mandatory Admissions Code."
The new code aims to make the process fairer, by stamping out unfair practices such as schools interviewing parents and pupils, or asking for personal information about the youngsters' family background in order to select pupils.
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