From September, three- and four-year-olds in England will be entitled to 30 free hours of care per week in term time - up from the current 15 hours.
But a poll of local authorities by the Family and Childcare Trust found uncertainty about impact of the policy.
There were concerns the change may lead to higher fees for additional care.
The survey was sent to all 152 local authorities in England, and 112 of them responded.
Of the 112, over half (54%) said they did not know if they would have enough childcare available for eligible pre-schoolers using the 30 hours.
A third (33%) said that there would be sufficient places, while a further 13% said there would not be enough.
More than two-thirds (67%) said they thought some childcare providers in their area would not offer the entitlement to 30 free hours of care.
Higher fees possible
The poll also asked if councils thought the new policy would lead to a reduction of quality in early years education.
Two-thirds (66%) reported that it would make no difference, 32% were unsure and 2% felt quality would be affected.
The survey also addressed the issue of cost and whether the new entitlement would lead to increased costs outside of the free hours available.
More than half (56%) did not know if there would be increased costs for three- and four-year-olds, while 63% were unsure if it would lead to higher costs for children aged two and under.
More than a third (37%) said it would increase costs for three- and four-year-olds, and 23% said it would do so for younger children.
The report says: "There was a lack of certainty about the availability of the 30-hour offer for eligible families.
"A clear majority of local authorities expect some settings not to offer the 30 hour entitlement - presumably because it would not make financial sense for them to do so.
"Until the policy has been introduced in full, it is difficult to predict how many settings this will apply to: it is likely that the pattern will vary in different parts of the country based on the comparative price paid for funded and non-funded places, and settings' ability to attract parents without offering the free entitlement.
"Despite this uncertainty, the majority of respondents believe that the 30 hour entitlement will enable more families to access childcare which meets their needs."
The report comes days after a study by the Institute of Economic Affairs recommended the 30-hour entitlement be scrapped in favour of a scheme for disadvantaged children.
30 hours free childcare for working families
- the 30-hour extension is available to families where both parents, or one parent in lone parent households, earn more than the equivalent of 16 hours per week at the national living wage
- there is an upper income threshold of £100,000 per parent per year, although couples who earn more than this between them will still be able to access the extension
- parents who do not meet the work criteria will continue to access the current universal offer of 15 hours free childcare a week in term time
- the scheme was piloted, in whole or in part, in some areas of England during 2016-17.
Ellen Broome, deputy chief executive of the trust, said: "While working parents are pleased to receive more hours of free childcare, they are not willing to cut corners on childcare quality.
"As this policy rolls out, the government must make sure that all families are able to access the high quality, affordable childcare that they need."
A Department for Education spokeswoman said helping families with high quality, affordable childcare was at the heart of the government's agenda.
"A number of areas are already delivering our 30-hour childcare offer, which almost 5,000 parents are benefiting from, and just recently we announced £50m to create nearly 9,000 new places.
"When the scheme is rolled out nationally, around 390,000 working families will be eligible, and, in many cases, these children are already in existing childcare places, which they will simply get for free when our offer goes live from September."
Cllr Richard Watts, chair of the Local Government Association's Children and Young People Board, said councils were concerned that the government's proposed increase in funding would not be enough to secure provision for everyone who wanted it.
"Government must use the learning from local areas that have been piloting the offer to ensure that there is no reduction in the quality of early education and care provided.
"When the offer is rolled out across the country, councils will need to have both adequate funding and sufficient local flexibility to work with their providers to ensure that all families have access to high quality care that meets their needs."
-reprinted from BBC