Academics at the London School of Economics (LSE) analysed the government's National Pupil Database figures to find out whether children were taking up places as soon as they were eligible.
Looking at how many autumn-born four-year-olds attending pre-school education in January 2011 had attended an early years setting when they were first eligible in January 2010, they found that almost one in five children (18.4 percent) had not.
Around one third of persistently poor children delayed, compared with one sixth of their higher-income peers.
Researchers found that persistently poor children who claim free school meals for all three years of early primary school are 13 percentage points less likely to attend for the full five terms of free pre-school education than children from higher-income families who never claim free school meals.
Meanwhile, children who speak English as an additional language are nearly three times more likely not to take up their full five terms as children who speak English at home.
The data predates last September's extension of the free entitlement for three- and four-year-olds of working parents to 30 hours.
But researchers concluded that the 30 hours initiative looks set to further widen the social mobility gap between rich and poor children.
"The new extension of the free entitlement to 30 hours applies to children of working parents only, while age eligibility will follow the same rules as the 15 hours," the LSE research concludes.
"Thus an autumn-born child in a higher income working family will benefit from five terms at 30 hours compared to three terms at 15 hours for a summer-born children in a family whose parents are unemployed.
"Without serious attention to this issue, the universal free places, while hailed as a great success in the prevalent policy discourse, look set to play a part in embedding or widening inequalities, in direct contrast to stated policy aims."
Neil Leitch, chief executive of the Pre-school Learning Alliance, said children from disadvantaged families are being further harmed by underfunding of the 30-hour offer, which is forcing providers to put in place additional charges.
"Despite the government continuing to stress the need to improve social mobility, here we have yet more evidence that the so-called free entitlement schemes in this country disproportionately benefit more-well-off families," he said.
"Add to this the fact that such schemes exclude the most disadvantaged families altogether while being open to couples earning up to £200,000 between them, and that sustained underfunding has led many childcare providers to rely on additional charges, meaning that often parents aren't able to access genuinely 'free' hours, and it's clear that the government is at risk of embedding inequality into the heart of its flagship policy."
The LSE research also indicated that Sure Start centres have been vital to increasing take-up of free early hours entitlements among disadvantaged families.
In areas where more children take their places in children's centres, take-up of early years education was highest among all children and the gap between low and higher income children was found to be small.
In contrast, areas where most pre-school places are through private providers have the largest gap in take-up between low and higher income families.
Between 2009/10 and 2017/18 the number of children's centres in the 30 per cent most deprived areas has been cut from 1,925 to 1,599, research by the Sutton Trust, published in April revealed.
"Universally funded pre-school education is not, in fact, being accessed equally by all children," said Dr Tammy Campbell, the author of the LSE early education research.
"The families who are benefitting most from the policy are those who are already advantaged in many ways - while low-income children miss out.
"The recent introduction of more free hours for parents earning up to £100,000 per annum is likely to worsen this situation, as well as closures of accessible provision in the state and voluntary sectors, including Sure Start centres.
"It's time for a clear and transparent reassessment of the purpose of funding for the pre-school stage - looking properly at which children win under the current system, and at who misses out."
Commenting on the LSE research children's minister Nadhim Zahawi said: "This government is doing more than ever before to support parents with the cost of childcare. We introduced - for the first time - 15 hours of free childcare for the most disadvantaged two-year-olds, which is being taken up by over 70 per cent of families.
"We increased universal free childcare for three-and four-year-olds to 15 hours a week and introduced an additional 15 hours of free child care for working parents.
"Those who aren't eligible can also access a range of other benefits - for example parents who work a few hours a week may be eligible to claim back 85 per cent of their childcare costs through Universal Credit.
This means that we will be spending around £6bn a year by 2020 to help make sure that every child, regardless of their background, gets the high-quality childcare that they deserve."