Research conducted for the Department for Education by Frontier Economics and the University of East London found that among more than 1,700 providers across 12 local authority areas, 39 per cent had experienced a reduction in their profit or surplus due to offering the extended hours, which are funded by the government.
Under the government's 30 hours childcare initiative, around 330,000 three- and four-year-olds have had their funded childcare entitlement doubled from 15 to 30 hours a week since September 2017.
Early years organisations and MPs have previously warned that government funding for the flagship initiative does not cover the full cost.
Researchers compiling the report on the first year found that 62 per cent of providers charged a higher hourly fee for parents than they received in funding. As a result, 41 per cent of providers had increased their hourly rate parents have to pay for childcare above the 30 hours.
The research also revealed more than half of providers (56 per cent) had introduced extra charges to make up for losses, for additional items such as lunch and snacks. Meanwhile, almost half of the settings offering the scheme (48 per cent) were also placing restrictions on when parents could take up the funded hours.
The report concluded: "The offer was not completely flexible or free for all parents."
Despite some experiencing financial losses, providers told researchers they offered the scheme for fear of parents leaving their setting if they did not.
One provider told researchers: "We felt that by turning the 30 hours away we were going to lose business, even though we were taking a drop in the money that was coming in, we still had to offer [extended] places."
Pre-school Learning Alliance chief executive Neil Leitch said it was time for the government to "face facts" about the unsustainability of the 30 hours scheme.
The alliance's own survey published last week found four in 10 childcare providers were fearful of having to close within the next year, as a result of the policy.
"This simply isn't sustainable and for the government to continue to insist that all is fine when study after study and survey after survey say otherwise is irresponsible to the extreme," he said.
"It's time for ministers to face facts and start working with the sector to try and salvage this policy and ensure that it is, in fact, viable in the long term."
National Day Nurseries Association (NDNA) chief executive Purnima Tanuku pointed to evidence in the report that suggested disadvantaged children were less likely to take up the offer, and as a result, were bring further disadvantaged.
Researchers found special educational needs and disability budgets were already inadequate to meet demand from children who were taking the universal 15 hours and could not be stretched to cover extended hours, while the registration process for the scheme was complex and "believed to be a barrier for parents who may face difficulties in navigating the system".
"NDNA is extremely concerned that current childcare policy is extending the gap between disadvantaged children and their peers," said Tanuku.
"Our members tell us that there is little or no support available to them locally for children who need the most help and for whom high-quality early years education is the most beneficial.
"Nurseries will be really worried that a comprehensive evaluation of the policy fails to mention the negative impact that rising delivery costs coupled with stagnating funding rates," she continued.
"If the funding is unsustainable then providers won't be able to offer the places that the policy needs, putting the whole project at risk."
Professional Association for Childcare and Early Years (Pacey) chief executive Liz Bayram echoed the concerns and warned that with the current situation, it was unlikely parents would be able to access 30 hours places in the future unless the government increased investment in the scheme.
Pacey's own research from August suggested two out of every five childminders are worse off for providing childcare under the entitlement.
Children and Families minister Nadhim Zahawi said the scheme is helping parents to increase their working hours, work more flexibly and spend less on childcare.
"Working families of every kind are reaping the benefits, including single mums and parents from lower-income backgrounds, who all told us their children's development had come on leaps and bounds by spending time in free childcare," he said.
"Providers have stepped up to the plate to deliver the offer which is having a significant positive impact on families' lives."