The primary school population in England has continued to rise sharply, with 94,000 extra pupils this year, reaching the highest levels since the 1970s.
The 2.1% increase in primary numbers is equivalent to six more pupils for every school.
"Minority ethnic pupils made up 71% of the increase," says the Department for Education's school census report.
The annual figures show there are now more super-sized primary schools.
It will mean more funding demands to create extra places and pressure on places for families looking for schools.
There are now 87 primary schools with more than 800 pupils, up from 77 in 2014 and 58 in 2013.
The number of infants in classes above the limit of 30 pupils has increased again - with 100,800 pupils in these over-sized classes, an increase of 8% compared with 2014.
The number has more than doubled since 2012, when there were about 47,000 infants in classes of more than 30. In 2008, the figure was fewer than 25,000.
The figures from the annual school census show numbers rising across the state school system - up by 2.1% in primary and 0.1% in secondary - to a total of 8.4 million pupils.
This is an increase of about 200,000 children in two years.
The rising population has been a particular challenge for primary schools, which have been having to expand to absorb the increasing numbers.
But this rising population wave has now reached secondary schools.
The analysis says that the rise in primary school numbers is particularly driven by rising number of ethnic minority pupils, accounting for more than two-thirds of the increase.
In primary schools, 30.4% of pupils are from an ethnic minority, compared with 29.5% the previous year.
But there are wide regional variations. In the inner London boroughs, 81% of pupils are from ethnic minorities; while in north-east England, the figure is below 11%.
And at council level, in Newham 94% of pupils are from ethnic minorities, while in Durham the figure is below 5%.
In inner London, the biggest ethnic group in primary school are black pupils, predominantly from an African background, with Asian pupils the second biggest group.
In secondary schools, about 27% of pupils are ethnic minorities, which the report says represents an increase of about 30% in six years.
Despite the rising number of pupils there has not been a growth in the number of primary schools, which have been consistently falling since the 1980s.
Instead, primary schools have been getting bigger, with more pupils in schools with more than 800 pupils.
Primary pupil numbers had been declining until 2009, but they have been rising sharply since.
'Good local school'
Funding this demand for extra places - forecast to be another 460,000 during the next five years - has been a continuing pressure on the schools budget.
In the general election campaign, the Conservatives committed themselves to protecting per-pupil spending, including for rising numbers.
A DfE spokesman said: "The average infant class size has remained stable at 27.4 and the number of unlawfully large infant classes has fallen - down 137 compared to 2009 - all despite a small increase in pupil numbers since last year.
"To help schools respond to rising pupils numbers, the government invested £5bn between 2011 and 2015 to support local authorities - creating almost half a million new places.
"On top of that, we have committed to invest a further £7bn on new school places over the next six years, to support the new school places needed all the way up to September 2021.
"The government has also opened over 250 free schools since 2010 and we are committed to creating at least 500 more during this parliament, creating over 400,000 new school places and ensuring even more parents have access to a good local school for their child."
Tristram Hunt, Labour's shadow education secretary, said: "The growing pressures on primary school class sizes should compel the government to rethink how it is allocating funding for schools.
"The case is clear. In the early years of primary school, children in classes capped at 30 are more likely to make better progress.
"It cannot make sense for the government to continue to prioritise money for new free schools in areas with surplus school places when we have more than 100,000 primary pupils being taught in classes of more than 30."