Government action to prepare schools for a predicted influx of pupils from the private sector is being demanded.
The economic downturn has forced some independent schools to close and experts say a growing number of parents are struggling to pay education fees.
Susan Kramer, Liberal Democrat MP for Richmond, in south-west London, has warned councils will need extra money to deal with any increase in numbers.
The government said state schools would be able to cope with any extra demand.
The number of children in private education dropped by 11,000 the last time the UK went through a recession in the early 90s.
A decade later, one in ten councils has revealed an increase in parents who want to move their children into state education, but many schools are already oversubscribed.
"We've got to make sure... that we can take these additional children, giving every one of them a quality education"The findings were published in an Audit Commission report last month into the effect of the credit crunch on councils in England.
The study found the higher demand for state school places was a particular problem in London.
Susan Kramer said: "We've got to make sure - bursting at the seams already - that we can take these additional children, giving every one of them a quality education.
"That's planning and it's money, and it needs to happen now."
A fifth of the councils questioned in the study expected the trend to accelerate as the downturn deepened.
Earlier this week, the Commons Children, Schools and Families Committee said the economic downturn could undermine investment in schools and children's services.
England's school building programme could be hit as private firms became less willing to invest, the committee added.
The government responded that funding was at record levels and school building programmes were being brought forward.
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