One in five primary schools and more than a quarter of secondary schools in England are either full or officially overcrowded, according to the Department for Education.
And experts are warning that children's education is increasingly suffering.
A combination of rising birth rates, immigration and a recession-fuelled exodus from private schools are taking their toll, particularly in large cities.
According to figures, nearly 100,000 children have been placed in state schools deemed as already full this year. Many are being taught in makeshift classrooms and temporary huts in playgrounds, and infant class sizes are already the biggest for 12 years.
The growing admissions crisis means nearly a third (29.3 per cent) of state secondaries – 916 schools – are full or have more pupils than they should, compared to 28.8 per cent in 2009.
One in five (20.3 per cent) state primaries – 3,444 in total – are also full or have more pupils than they are meant to cater for. This is up from 19.8 per cent, or 3,376 primaries, last year.
Primary head teachers are being forced to accommodate an extra 41,680 pupils. Infant class sizes are already the biggest for 12 years.
The coalition has acknowledged that the shortage of primary places is 'critical' and claimed the previous Labour government failed to make adequate preparations for the extra pupils despite warnings.
More than 1,000 primary schools have closed since 1999.
Last month education secretary Michael Gove warned that primaries will have to find room for an extra 350,000 pupils over the next four years.
This is because an increase in the birth rate has boosted demand for places by about 15 per cent a year.
But Migrationwatch claims that 550,000 more school places will be needed by 2016 to help educate the children of immigrants.
Over the next decade, it estimates that this will rise to one million extra places - at a total cost of about £100billion.
Chancellor George Osborne announced last week that the schools' budget will rise from £35billion to £39billion over the next four years - a 0.1 per increase in real terms annually.
But analysis by the Institute for Fiscal studies suggests funding per pupil will fall in real terms by 0.6 per cent a year because of expected increases in numbers.
Professor Alan smithers, director of the centre for education and employment research at Buckingham University, said it will lead to a 'poorer quality of education' for many, he said.
He added: 'Governments to a large extent get five years warning of the number of places that are necessary.
'Almost certainly, this will mean less personal attention for each child.'
A Department for education spokesman said last night: 'We are aware of a shortage of places at primary level in some areas.
'This is something that has been looming for a few years. Local authorities are responsible for planning ahead to ensure they have enough places and we will work with them to ensure sufficient room exists.'