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.
A poll of local authorities by the Family and Childcare Trust found that over half of the councils who responded did not know if they would have enough childcare for eligible pre-schoolers using the 30 hours.
A third said they would have enough places, while a further 13 per cent said they would not have enough.
Councils in South Yorkshire said they are working with childcare providers to ensure that there are enough places.
Sheffield Council said it will be able to meet the extra demand.
A council spokesman said: "We are working with nurseries and childcare providers to make sure that we can provide the extra childcare places needed in September.
"Looking at the numbers of childcare places that are already delivered we will be able to meet the extra demand in the autumn and spring terms.
"In the summer term we expect there to be a higher level of demand for childcare places and so are working with the providers and plan to meet these needs.”
Doncaster Council said it was 'actively working' with childcare providers and has received £1.8m of funding to help create additional places.
Damian Allen, director for Learning and Skills at Doncaster Council, said: “All local authorities are planning for the increase in child care provision hours from 15 hours a week to 30.
In Doncaster we are doing the same and to ensure that we are prepared, in 2016 we successfully secured £1.879m of funding from the Department for Education to help create additional places.
“We are actively working with schools, private providers and childminders to help them make sure they are ready and have the relevant resources in place to encourage parents and carers take up this new entitlement.
“This is a positive new provision that will not only help parents and carers but will ensure children are experiencing happy and caring child care environments which will in turn prepare them for the start of their school experience and help them thrive.”
Rotherham Council has launched a consultation to find out how many families in the area would want to take up the offer, so it can ensure there is enough capacity.
Ian Thomas, Strategic Director of Children and Young People’s Services at Rotherham Council said: “Rising childcare costs can be a barrier which prevents some parents, and particularly mothers, from working.
“We now need to make sure the places which may be needed are available and parents have access to this, should they want it."
To take part in the consultation, which will run for a month, visit www.rotherham.gov.uk/homepage/64/open_consultations