More than £2m will have to be spent on extra classrooms in Bristol primary schools to cope with more pupils.
The demand is believed to be due to increased births, immigration and parents not being able to afford places at private schools.
More than 4,500 four-year-olds in the city are starting school in September.
Councillor Clare Campion-Smith said the cash, more than double what was budgeted for, would be taken from other budgets to pay for more classrooms.
Due to the recession, fewer middle class parents have been able to afford private school fees, so are instead turning to the state, council chiefs said.
'Better than before'
Liz Haydon-Turner, of campaign group Bristol Primary Admissions Crisis, said the situation was better this year than previously.
She said: "Every family has been offered a school but there are pockets all over the city where people haven't been offered a school near their home or that's one of their three preferences."
Temporary classrooms were put in place last year and more were needed this year, she added.
Ms Campion-Smith, Liberal Democrat cabinet councillor for children, said that at this time in 2009 there were 300 families who had no offer of a school place near their homes.
She said the council had promised that would not happen this year.
She added: "It does take time to get new schools such as at Ashley Down, up and running. The long-term planning is in process but in the meantime, we have got to make sure we have have the right accommodation as close as possible to the people who need it.
"We do still have people who are travelling further than we would like."