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Nearly 100,000 infants are in primary school classes larger than the planned maximum, Labour claims.
Shadow education secretary Tristram Hunt said the number of five to seven-year-olds in classes of over 30 children has "spiralled by 200% since 2010 - to nearly 100,000 infants".
The Government says it is "making every effort" to prevent class sizes increasing, despite an "unprecedented increase in pupil numbers".
A Department for Education spokesperson said £5 billion had been given to councils to spend on new school places over the course of this Parliament - prompting the creation of 260,000 new school places in shortage areas, "with more planned".
"We have also confirmed a further £2.35 billion to support councils to create the places needed by September 2017, and are allowing good schools to expand without the restrictions and bureaucracy they faced in the past."
The spokesperson added that children are only allowed to join classes of 30 or more in "exceptional cases", adding that the proportion of primary pupils in classes over 36 in size had fallen since the coalition took power.
Parents are worried about the impact increased primary school class sizes could have on their child's education, a new poll indicates.
A survey of more than 1,700 parents by Netmums found that more than half (52.7%) wish their children were in smaller classes.
Almost a quarter (23.9%) said they were worried their children would suffer academically because of overcrowding in classrooms.
Among the concerns raised by parents were fears of a lack of equipment, a negative impact on discipline and children not receiving enough attention from staff.
Netmums founder Siobhan Freegard said: "Although some kids will flourish in a busier environment, many parents feel that increased class sizes and number of classes leads to their child being 'forgotten' - and to parents feeling less involved in this vital time of their little one's life."
Councils have been forced to cut back on school repairs, building projects and to borrow money to plug a £1 billion black hole in funding for school places, it has been claimed.
More than three quarters of authorities in England say they have not received enough money from the Government to create the extra school places needed in their area in a five-year period to 2016/17, according to a poll by the Local Government Association (LGA).
It warned that local councils are facing a challenge in creating places on time and in the right areas at a time when they are also short of cash to do so.
The findings, published just weeks before children across the country head back to school for the start of the new academic year, come amid a continuing concern about a squeeze on school places that has been fuelled in part by a rising birth rate and changes in local populations.