The Childcare Act 2006 places a duty on local authorities to ensure working parents, and those undertaking training and education with a view to returning to work, can access childcare.
But the figures show that only 20 per cent of local authorities in England are providing sufficient childcare for children aged up to two.
Fifty-three per cent of authorities in England are delivering enough early years provision for three- and four-year-olds, but just 14 per cent – one in seven – are meeting requirements for disabled children.
In Wales, the results are slightly better for two-year-olds, with 25 per cent of councils meeting their target. But only 38 per cent of Welsh authorities were providing adequate care for three- and four-year-olds.
The Daycare Trust merged at the start of this year with the Family Parenting Institute. Its chief executive Anand Shukla described the results as a “national scandal”.
“Councils across England and Wales are failing families by presiding over a continuing shortage of high-quality, affordable childcare,” said Shukla.
“At a time when one in five children lives in poverty, the failure to provide this essential service for parents who want to provide for their families is a national scandal.
"Local authorities have a legal duty to ensure a sufficient supply of childcare in their areas, but no doubt their failure to do so is linked to the tight financial squeeze they find themselves in, with ever more austere funding settlements.”
Shukla also called on the government to invest more in providing support for parents, since the childcare that is available is becoming unaffordable for parents.
He highlighted research from the Department for Work and Pensions that showed a third of parents who want to work more are unable to, because they cannot find affordable childcare.
Debbie Jones, president of the Association of Directors of Children's Services, said the weak economy had put pressure on early years providers.
"Early years providers have been understandably reluctant to expand their businesses in the current economic climate,” said Jones.
“This is not helped by the two-year-old childcare offer funding currently being limited to one year, which offers no long-term funding assurance to these providers. This impacts on the level of provision available in local areas.
“While it may be ideal to have more local authority-funded places available, councils are having to make tough choices with the limited funding they receive from central government."
The findings were collected for the Daycare Trust and FPI’s Childcare Costs Survey 2013, which will be published later this week.