Research commissioned by the Pre-school Learning Alliance has found that the number of children currently meeting the eligibility criteria for the 30 hour offer, which comes into effect in September, is 478,000 - 23 per cent higher than the government's estimate of 390,000.
The study, conducted by independent research agency Ceeda, estimates a further 22,000 children on top of this could become eligible for the offer if parents in working households make relatively small changes to their work patterns, bringing total eligibility to around 500,000 overall - 28% higher than the government's estimate.
On the back of the findings, which were based on a survey of 1,708 households, the Pre-school Learning Alliance has warned that tens of thousands of parents could miss out on the 30-hour funded childcare offer due to a lack of available places.
Neil Leitch, chief executive of the Pre-school Learning Alliance, described the study findings as "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," he said.
"Add to this the fact that many providers are warning that they are planning to either limit the number of 30-hour places they offer, or opt-out of the scheme all together, and it's clear that the government is heading for a childcare capacity crisis.
"The government must do more to support early years providers if the 30-hour scheme is to have any chance of working in the long-term. That means both adequately funding the creation of enough new places, and ensuring that the free entitlement offer in general is funded sufficiently in the long term.
"Thirty hours of so-called ‘free childcare' may sound like a great policy, but 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."
Last week Education Secretary Justine Greening announced that a grant scheme worth £50m has been set up by the government to create 9,000 more childcare places ahead of the expansion of free provision later this year.
Under government plans, all three- and four-year-olds will be entitled to 30 hours of government-funded childcare each week from September 2017.
The DfE has been contacted for comment.