The government has underestimated the number of children in England eligible for 30 hours of free childcare promised from September, warns a lobby group.
The government says 390,000 three and four-year-olds will be eligible.
But research for the Pre-school Learning Alliance suggests the figure will be nearer 500,000, meaning tens of thousands could miss out.
The government says it is spending more on childcare than any previous administration.
It will "hit the ground running" to deliver the extra free hours in September.
The government already funds 15 hours of free nursery care for three and four-year-olds.
This is due to rise to 30 hours for working parents from September.
The basis of the Pre-school Learning Alliance (PSLA) warning is twofold:
a survey of 1,700 households suggests the proportion of children meeting the eligibility criteria is 23% higher than government estimates
the government has not allowed for parents increasing their working hours to become eligible for the scheme - to qualify, each parent must earn a weekly minimum equivalent to at least 16 hours at the national minimum wage.
The specialist early years research company Ceeda, which carried out the survey, says an extrapolation of the results suggests 478,000 children meet the eligibility criteria.
The researchers say that parents increasing their hours could add another 22,000 children, bringing the total to about half a million - 28% higher than allowed for by the government.
And the PSLA says the final figure could be even higher as the Ceeda calculations do not include children of parents not currently working who take up jobs, encouraged by the offer of free childcare.
The group says that if children meet the eligibility criteria and their parents can find nurseries offering the free hours, the government will have to fund them, even if there are more of them than they have allowed for in their budget.
PSLA chief executive Neil Leitch called the figures "deeply concerning".
"The Department for Education has been clear that the whole point of restricting the scheme to 'working families' is to encourage parents to go back to work, yet they don't seem to have factored even the most modest of adjustments into their figures, such as parents working a few more hours to become eligible."
The latest PSLA warning follows earlier concerns that the hourly rates paid to nursery owners for free hours do not cover costs.
A report by the National Audit Office last March warned that some childcare settings might choose not to offer the extra free hours "if the funding is not right" as this might threaten the viability of their businesses.
And one nursery owner, who spoke to the BBC in October, warned: "We'll go bust under the current proposals."
Neil Leitch said the two factors together could lead to "a childcare capacity crisis".
He said that while 30 hours of "so-called 'free childcare' may sound like a great policy... if there aren't enough places to match demand and the government continues to refuse to listen to valid concerns over funding, the policy simply cannot succeed".
A Department for Education spokeswoman said the government would be spending a record £6bn on childcare by 2020, including an additional £1bn on the free hours.
"Around 390,000 working families will be eligible for 30 hours free childcare from September. In most cases, their children are already in existing childcare places, which will become free.
"We are also creating almost 9,000 new places through £50m of capital grants," said the spokeswoman.
-reprinted from BBC