A "haphazard approach" to admissions is denying families a real choice over where their children go to school, according to school leaders.
The NAHT headteachers' union said that the lack of a clear system for awarding places means that parents have to hope they "get lucky".
It is calling on the government to create a national strategy to guarantee that there are enough school places for England's schoolchildren.
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The call comes on deadline day for families in England to submit applications for primary school places, for children starting this September.
Under the current system, parents list up to six preferences on an application form, which is submitted to the local council.
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But there are concerns in some quarters that while local authorities are responsible for ensuring that there are enough state school places in their area, many of their powers to create new schools and direct schools not under their control to expand have been curtailed.
Paul Whiteman, NAHT general secretary, said: "Deadline day can be an anxious time for families. Choosing the right primary school and securing a place can feel like a shot in the dark for parents.
"The reality is that until we have a coordinated approach to place planning, parents will still have to hope they get lucky.
"Local authorities are responsible for ensuring sufficient school places, but their powers and resources were removed in 2011 and not replaced with an alternative.
"Instead we have decisions being made in isolation and new schools and new school places are not always being commissioned in the areas they are most needed.
"This haphazard approach the government favours is denying parents and families a true choice over where to send their children to school."
He cited official government pupil projection figures, which estimate that the secondary school population will be 418,000 higher in 2027 than in 2018 – a 14.7 per cent increase in pupil numbers.
"There is a desperate need for long-term planning that spans all sectors and until the government creates a national strategy to guarantee there are enough school places for every child in England, choice for parents will continue to be a bit of an illusion," Mr Whiteman said.
England's school system has been put under pressure in recent years due to a rise in the school-age population.
This has been fuelled by an increase in the birth rate in the early 2000s that has now made its way through primary schools and is moving into secondaries.
Department for Education statistics show that in 2019, 90.6 per cent of children got offered a place at their first choice of primary school.
The DfE has previously said it is creating more school places, in part through its free schools programme, and especially in areas that need them most.
School standards minister Nick Gibb said: "Choosing a primary school for your child can be a difficult decision but it has been made easier for parents who are now significantly more likely to have a 'good' or 'outstanding' school on their doorstep than they were 10 years ago.
"We have also made sure that the supply of school places meets demand, meaning that last year the vast majority of parents got their first choice of primary school or another of their top three choices. It also means we have managed to keep primary school classes broadly stable in size despite a large increase in pupil numbers."
Judith Blake, chairwoman of the Local Government Association's Children and Young People Board, said: "This time of year can be extremely stressful for parents and carers choosing the right school as everyone wants their child in a school where they can be happy, safe and reach their full potential.
"Councils have been able to provide more than 800,000 desperately needed places for those looking to secure their child's place at a primary school in the past decade despite not having control over planning for places.
"Councils need to be allowed to open new schools and have a final say where they are placed, as well as to direct academies to expand. It makes no sense for councils to be given the responsibility to plan for school places but then not be given any control.
"The government needs to work closely with councils to meet the challenges currently facing the education system."