Nearly 3,000 pupils are at risk of not having a school place in 2016 after a recent boom in births and increased demand for Sutton's high-achieving schools.
Forecasts show there will be 1.2 pupils for every available primary school place in Sutton by the start of the 2016/17 academic year.
There is an expected shortfall in the number of places available to the borough's pupils from this year but Sutton Council says it is making up for this through schools taking on extra permanent classrooms and 'bulge' classes, often housed in portable buildings on schools sites.
But the council has refused to comment on its plans to cope with the increased demand beyond this year and whether or not a new primary school could be built in Sutton.
Figures released by the Local Government Association (LGA) show there are 14,104 places in Sutton Primary Schools and last year there were 13,992 pupils. T
he LGA forecasts there will be 15,589 pupils in the intake starting this month and 16,938 by 2016/17 - meaning a shortfall in available places of almost 3,000.
A council spokesman said: "Sutton Council has a programme of school expansion which has been in place since 2010.
"Since 2010, 18 permanent classes and 18 bulge classes have been added. For September 2013, seven new permanent classes have been added across three schools.
"We have been and will continue to monitor future growth and will act accordingly to ensure that Sutton Council fulfils its responsibility to provide school places for children resident in the borough.
"Sutton has been popular with parents for many years due to the high number of outstanding schools in the borough producing consistently excellent results."
Sutton, along with Croydon, has one of the largest predicted shortfalls in primary school places in the country but many other areas are facing deficits.
The LGA is calling on the Department for Education to do more to let councils explore solutions on a regional level.
Councillor David Simmonds, chairman of the LGA’s children and young people board, said: "Local councils have a legal duty to ensure there is a school place for every child in their area but they are being hampered by uncertainty and unnecessary restrictions.
"This could result in parents scrambling for places that just don’t exist and threatens to seriously impact on our children’s education."