More than half a million primary school children are now being taught in "super-size" classes, Labour has warned.
Thousands more youngsters are in classes of more than 30 pupils, the party said, while the number of so-called "titan" schools has soared in the last five years.
The figures come on the deadline day for parents to submit applications for children starting primary school in September.
Shadow education secretary Lucy Powell blamed the hike in class sizes on the Government's flagship free school programme, arguing that the initiative has made it harder to ensure there are enough school places around the country.
Free schools are semi-independent state schools that are not under local council control.
But a Conservative Party spokesman said that 500,000 more school places have been created and accused the last Labour government of cutting funding by £150 million, scrapping almost 200,000 places.
Labour said that its analysis of official Government figures shows that: "Over half a million children are now in super-size classes in primary schools, as class sizes continue to rise."
Overall, 520,445 children aged between five and 11 are being taught in classes of at least 31 pupils, the party said. Of these, 38,560 are in classes of 36 or more children and 14,824 are in classes with at least 40 youngsters.
In 2014, there were around 500,514 children in classes of more than 30 pupils, Labour said, meaning that the numbers have gone up by 19,931 in the space of 12 months.
Labour added: "There are also over five times as many 'titan' primary schools - those with over 800 pupils - than there were in 2010." These numbers have risen from 16 in January 2010 to 87 in 2015, the party calculated.
Over the same period, the numbers of infants (five to seven-year-olds) in classes of 31 or more has risen by 224%, from 31,265 to 101,270.
A limit on infant school class sizes was introduced by Labour in the late 1990s, stating that no more than 30 youngsters should be in a class.
But under the rules, there are certain circumstances in which schools can legally waive the limit, and these have been extended in recent years, for example to allow classes to be made larger to take in twins, or the children of those serving in the armed forces.
Ms Powell said: "The Government's obsession with free schools, at the expense of opening other types of school, has made it harder and harder to ensure there are enough school places everywhere.
"This approach is clearly not working for parents up and down the country, with the result that come national offer day, some families applying today will go straight on to a waiting list with no offer of any school place and soaring numbers of children will continue to be crammed into ever-expanding classes, as the only option left for many schools in many areas.
"The current system for planning new places is essentially broken.
"It is now time for the Tories to abandon their unjustified fixation with free schools, which are evidently not addressing the growing pressure on school places nor driving up standards, and once and for all, put the urgent need for sufficient good school places in every local area first."
A Conservative spokesman said: "At the same time as pupil numbers were booming, the last Labour government cut funding for school places by £150 million, scrapping almost 200,000 places.
"So rather than trying to scare parents with misleading statistics, they should be backing the measures we've taken to clear up the mess they left behind
"Under the Conservatives, funding for basic need has been doubled, creating 500,000 more school places.
"On top of that, because of the difficult decisions we've taken elsewhere, we'll be able to invest £23 billion in school buildings over the course of this Parliament, creating hundreds of new schools."
The Local Government Association (LGA) today warned that it must be given the powers to open new schools or force academies to expand in order to meet the demand for school places.
Councillor Roy Perry, chairman of the LGA's children and young people board, said: "Councils have a statutory duty to ensure every child has a school place available to them but find themselves in the difficult position of not being able to ensure schools, including academies, expand.
"Finding suitable sponsors with the capacity to take on the running of a successful new school is also proving a challenge."
Labour's figures also indicate that the South East has the highest number of pupils in primary classes of 31 or more at 89,116 youngsters, while the North East has the lowest at 18,122.
Christine Blower, general secretary of the National Union of Teachers, said: "The need for more school places has been known over many years.
" A key duty of government is to ensure there are sufficient school places and enough qualified teachers. The Government has failed on both, thereby letting down children and parents.
"This situation could have been avoided by allowing councils to build schools in areas where additional school places are needed.
"The Government has poured money and resources into the wasteful and indulgent free schools programme, many opening in areas where there is no need, and many providing only a small number of places at vast cost.
"The Government must produce sufficient funding and powers for local authorities to open more schools as a matter of urgency."
The National Association of Head Teachers (NAHT) said the current system risked harming children's education and "over-stretching capacity" could see teaching standards suffer.
NAHT general secretary Russell Hobby told the BBC: "Since 2011, the powers of local authorities in planning school places have been significantly reduced without an alternative system to take their place.
"There is a desperate need for long-term planning that spans all sectors ... we cannot afford inefficiency and conflict."