London needs '118,000 extra school places' in three years
The body that represents London's 33 local authorities says at least 118,000 more state-funded school places will be needed within the next three years.
London Councils is calling on the government to allocate more money to help boroughs cope with the demand.
Ministers say they are already spending £5bn over the next two years to create more school places across the country.
The cost of providing enough school places for children in London is expected to rise to £2.3bn by 2016.
The report by London Councils says the shortage is most acute in primary schools, but the need for secondary school places will rise as pupils get older.
London has a 52% share of the national demand on secondary school places and 39% of the national shortfall on primary school places.
Yvette Stanley, chair of the Association of London Directors of Children's Services, says hundreds of primary school classes and at least 22 new secondary schools will have to be built very soon.
The capital has received £576m for schools over the next two years, but London Councils says there remains a funding shortage of more than £1bn.
Councillor Peter John, London Councils' executive member for children's services, said: "It is simply staggering that the capital will get proportionately less funding compared with its need."
Demand for school places in the capital will increase from 90,000 places in 2015-16 to 118,000 places by 2016-17.
The Department for Education's new funding framework allows boroughs to bid for a share of the capital's schools budget, but London Councils says this puts boroughs in competition with each other.
The group says the process will deliver a fraction of the extra money needed, leaving already hard-pressed councils with the choice of finding the difference from other local budgets or going without.
Mr John said: "Kids need school places, not bureaucracy.
"Instead, we have another layer of government red tape which is preventing boroughs from getting on with building new schools."
A Department for Education spokesperson said: "More than £1bn extra has been spent on school places in London in the last year alone.
"This is on top of the £1.6 billion already available to help councils create places where they are most needed, and will cover the full cost of any project — whether that is a new build or an expansion.
"We are working with local authorities to ensure funding is targeted where it is most needed.
"By September, we expect 190,000 extra places will have been created across England, with many more still to come."
Census data shows that between 2001-11 the school age population in London increased by 107,000.
This is a growth of 8.2% between censuses, compared to a national reduction of 0.2%.