The research, carried out by the National Association of Head Teachers, revealed that only one fifth (19%) of the 425 providers surveyed thought the funding they received was sufficient to cover their costs.
Seventy per cent said they were cross-subsidising from another part of the school to enable them to offer additional hours.
Paul Whiteman, general secretary of NAHT, said cross-subsidies were “unsustainable”.
He added: “The government’s 30 hours free child care promise should be a boost to parents. But it is not truly free.
“We are seeing that providers are having to make up the funding shortfall by charging parents a higher rate for additional hours outside the school day, or for extras, like milk or nappies.”
Whiteman highlighted that funding pressures were disproportionately affecting children from disadvantaged backgrounds.
“Almost a quarter (24%) of our survey respondents felt that the 30 hours offer had displaced more disadvantaged three and four year olds only entitled to 15 hours of free child care,” he said.
“Help is not reaching the families that most need it, and children from the most disadvantaged backgrounds could risk being pushed aside.”
The NAHT called on the government to revisit funding rates for providers, ensure providers receive funding on time and carry out a full evaluation of the impact on the children excluded from the policy.
Roy Perry, vice chair of the Local Government Association’s children and young people board, said: “We have previously warned about the impact on quality, with a risk that insufficient funding will lead providers to employ less qualified staff or struggle to provide enough support for children with additional needs or disabilities.
“Councils 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.”
The 30 hours free child care policy was introduced in England in September 2017, by then education secretary Justine Greening.
Roughly 390,000 families in England were said to benefit from the scheme, which is backed by an extra £1bn annual funding by 2020.
A Department for Education spokesperson said: “We know the cost of child care can be a burden on families, which is why we are spending more than any other government on support – around £6bn a year by 2020 – to help make sure that every child gets the best start in life.”