On 1 September, the number of two-year-olds eligible for 15 hours of free childcare a week from a local provider will double from 130,000 to 260,000.
However an investigation by CYP Now has found that many authorities are not ready.
Of the 131 authorities that responded to a Freedom of Information request, 70 (53.44 per cent) said they will not have secured enough places to deliver the offer to all eligible children before next month’s deadline.
Together they report a shortfall of 34,854 places.
This means that only 185,000 of the 219,854 eligible two-year-olds across the 131 regions will have access to a free childcare place.
Extrapolated across all 152 local authorities, that data suggests that 218,782 two-year-olds will be offered a free place under the scheme, leaving a nationwide shortfall of 41,218.
The shortfall could be even larger because councils have admitted that 1,499 of the settings earmarked to provide places are yet to be rated by Ofsted.
Under the terms of scheme only settings rated “good” or “outstanding” will be funded to deliver free childcare.
Neil Leitch, chief executive of the Pre-school Learning Alliance, is concerned by the findings.
He said: “Local authorities have a statutory duty to secure sufficient funded early education places for all eligible children, so the fact that the majority of councils are still not meeting this target should be a real warning sign to government.”
Shadow childcare minister Lucy Powell said: “This is yet more evidence that ministers are failing to deliver on this important policy.
“Ministers have their heads in the sand and are more and more likely to fail the families who are expecting a place.”
In response to the findings, a spokeswoman for the Department for Education said councils are being supported to ensure the offer is delivered to as many eligible two-year-olds as possible.
The expansion of the scheme was announced by Deputy Prime Minister Nick Clegg in December last year.
Click here to download a PDF graphic of the data