More than 250,000 extra school places will be needed by next year to meet a continuing surge in demand, the spending watchdog has warned.
The rise in the number of children born in England between 2001 and 2011 was the largest 10-year increase since the 1950s.
This has led to an increase in demand for primary school places.
The Department for Education has increased the funding it provides to local authorities with a net increase of almost 81,500 primary school places in the last two years. More than £5bn has been invested into new school places since 2010.
However, there are still indications of a real shortage, the National Audit Office has found.
In May last year just over 20% of schools were full or over capacity despite the more than 80,000 extra places created between 2010 and 2012.
In the next two years 240,000 of the new places needed are in primary schools - 37% in London.
Julian Wood, Study Director at the National Audit Office said: "I think it's important to say that of the 256,000 (places) there has been a year's further work that hasn't been reflected in these numbers.
"The level of funding has increased to something like that which was originally expected to be needed and local authorities are working hard to deliver these places.
"Nonetheless, we think there's an awful lot more that needs to be done to help that money work as efficiently as it can if those 256,000 places are to be delivered."
The report authors say it's important the right amount of money gets to the areas that need it most to prevent part of a younger generation missing out on the first few crucial years of education.
Lindsey Barrett, manager of the Busy Bees nursery in Ealing, London, told Sky News: "Parents are worried that perhaps they are not going to get a school in their local area, or their first choice.
"Being a parent myself I am completely in empathy with those parents because it is a very big decision that is being made - it's their child's future education.
"Parents worry that if it is a school perhaps out of their area, or perhaps if any of the numbers increase in classrooms - that is looking at the education and the quality that they will be receiving.
"Sometimes parents might try and move out of the area, obviously do a lot of research into the local school they hope they are going to get there, that they are going to get one of their first choices, but it doesn't always happen.
"As a parent you always want the best education you can get for your child."