Thousands of four-year-olds are expected to miss out on their preferred primary school when offers are made today.
Last year, about 76,600 children did not get their top pick and more than 22,000 children did not get a place in any of their preferred primary schools.
Mary Bousted, general secretary of the ATL teaching union, predicted a similar outcome this year, describing the situation as a "failure" by the government.
"These children were born on the coalition’s watch and have been let down by a government that prioritised the ideological free school programme over ensuring that every child has a school place.
“We need to move to a system where local authorities can build and run schools, in order that they can fulfil their legal duty to ensure that every child has a place in a safe classroom, with a qualified teacher.
“Political parties often talk about parental choice in schools. Unfortunately for tens of thousands of parents this is an illusion; finding any local school place for their child is a challenge, let alone being able to choose one.”
Labour has also released data that it says shows the number of infants being taught in large classes has reached its highest level for 15 years. Its analysis of data based on Freedom of Information requests to 61 local councils indicates that nationally about 102,615 pupils aged between 5 and 7 are being taught in classes of at least 31 children.
Earlier this month the Local Government Association (LGA) warned the shortage of places was reaching a "tipping point", saying two in five council areas in England will not have enough primary school places by September 2016.
It said councils had created more than 300,000 primary school places since May 2010, but many had done so by diverting money set aside for school repair programmes or converting areas such as music rooms into classrooms. The LGA has argued that more cash and new powers to open schools are needed to help councils meet the demand.
The number of primary-aged pupils has been increasing since 2010 and is forecast to rise by a further nine per cent by 2023.
Previously, the coalition government said that it gave £5 billion of funding to councils to create new school places during the last parliament and a further £2.35 billion to continue to create the places needed by September 2017.
Schools pushed to ‘breaking point’ over squeeze on places, says LGA – 13 January, 2015
School places: Councils forced to cancel repairs to plug £1 billion black hole – 27 August, 2014
School places crisis: Councils forced to borrow millions to meet shortfall – 14 March, 2014