A surge in the number of four-year-olds will require primary schools to find an extra 350,000 places over the next four years, at a time when education spending is set to be cut by up to 20%, it was reported.
Education Secretary Michael Gove has been told by Whitehall officials that an increase in the birthrate has boosted demand for places by about 15% a year, reported the Daily Telegraph.
If confirmed, the figures would require the construction of hundreds of new schools, the use of portable classrooms or an increase in class sizes at existing primaries, potentially above 30 children.
Mr Gove has been asked by Chancellor George Osborne to identify savings of between 10% and 20% in his departmental spending over the next four years as part of the Government's efforts to pay down the bulk of its deficit within five years. This will limit the scope for him to order a large-scale school-building programme.
When he appears before Mr Osborne's spending "star chamber" later this month, he may cite the swelling primary school rolls as a justification for him being allowed to retain a larger share of his budget.
For the first time in a decade, the number of children joining the state primary system when schools returned from the summer holidays this week was larger than the previous year, said the Telegraph.
And the figure is predicted to rise by around 90,000 each year between 2011 and 2015, increasing the total population of state primary schools and nurseries from around 3,960,000 to 4,300,000.
In the decade from 1985, there was a "baby boom" which saw the birthrate increase for a few years, before declining again. Many of those born in that period are now having children of their own, and immigration has also helped push the birthrate in 2007 to its highest for 26 years.
Former teaching union official John Bangs, now a visiting professor at the Institute for Education, told the Telegraph: "Primary schools are in crisis. There is an absolute requirement on Michael Gove to fund these additional places - he has no choice. The Government cannot go in for the major reductions of the education budget it has planned."