Under new SNP legislation, families are entitled to a mandatory 600 hours of funded early learning and childcare for three and four-year-olds.
Councils deliver the policy by using part of their overall block grant to provide enough free places in state nurseries - or by paying partnership providers in the private sector if they cannot meet the demand themselves.
However, a survey by campaigning parents from Glasgow has shown hundreds of children are unable to secure fully funded places at the private nurseries they currently attend.
The poll, which secured responses from 65 partnership nurseries, found they had 1805 eligible children on their books, but only 1222 funded places - a shortfall of 583. The council argues sufficient places are available in other nurseries.
The issue has also impacted on parents in East Lothian where the council has capped the number of places it funds in private nurseries.
Parents said in some nurseries available funding was shared between families, while others said lots had been drawn to see who benefited.
The row has prompted calls for the Scottish Government to change the policy to ensure parents get funding wherever they send their children.
Purnima Tanuku, chief executive of the National Day Nurseries Association Scotland, said: "The current system greatly restricts the choice available when it comes to finding a nursery that suits family and working hours.
"We strongly believe the choice of which nursery receives the funding should be led by the parents rather than the local authority."
The Scottish Government said that every council had a legislative duty to consult with parents about where free places should be allocated.
A spokeswoman said: "Most local authorities have engaged with partner providers to ensure provision is in place for eligible children this year, but this can't always be guaranteed to be at parents' first choice of nursery.
"Local authorities are now required to consult with parents at least once every two years on the provision best suited to their needs which should introduce greater flexibility and choice."
The issue has arisen after parents at private nurseries in East Lothian and Glasgow started campaigns to secure funding for their children.
Both local authorities said sufficient places were available in the pre-school sector, but working parents argue council nurseries are not suitable because they do not provide wrap-around care and they close during school holidays.
Even if places are available in other private nurseries it still means parents cannot access funding without moving children at a critical stage in their development.
Shirley Hexley, the owner of Clarence House Nursery in Maryhill in Glasgow, said: "This is an entitlement all three and four-year-olds have been promised and it is just not being delivered to the satisfaction of working parents. The funding should follow the child."
Jennifer Gorevan, 38, whose three-year-old daughter Ava attends Clarence House, said alternative provision was not suitable. "It is incredibly frustrating to be told the nursery will not have enough funded places when it is perfect for our needs and there isn't a viable alternative," she said.
Stephen Curran, Glasgow's executive member for education, said: "We know this is an emotive subject, but the legislation says councils have a duty to provide sufficient places and does not specify that this is a nursery of their choice. We are not withholding funding."
A spokeswoman for East Lothian said: "A very small number of families may not be accommodated at their first-choice provider, but there will be a number of alternative options available."