This month the free childcare entitlement for working parents of three- and four-year-olds doubled to 30 hours. But The Sutton Trust is concerned that by offering the initiative only to working parents, children in workless families will fall further behind their peers when they start school.
The think-tank is also concerned that the offer's focus on quantity of hours comes at the expense of the quality of early education on offer.
In its report Closing Gaps Early, the trust calls for more investment in early years professional development to ensure all nurseries have access to early years teachers.
The trust is particularly concerned that a third of nursery staff do not have either English or maths, or both, at GCSE grade C or above.
"Good-quality early years provision is vital to narrow the gaps that leave too many youngsters behind by the time they start school," Sutton Trust chair Sir Peter Lampl said.
"But it's unlikely that the government's policy to provide 30 hours of free childcare will provide this.
"It is understandable that the government wants to improve access to childcare for working parents. But this must not be at the expense of good early education for disadvantaged children. It is the quality of provision that matters.
"Focusing on getting it right for the poorest two- and three year-olds would make a much bigger difference to social mobility, by improving their chances at school and in later life."
The report adds that the 30-hour offer has not been properly funded and is leaving early years providers with less money to invest in staff.
Earlier this month the New Economic Foundation claimed that nurseries offering the 30-hour entitlement would have to pay staff below the national minimum wage to break even.
Report co-author Kitty Stewart, who is associate professor of social policy and associate director of the Centre for Analysis of Social Exclusion, said: "Recent changes to funding for early education look set to have further damaging effects on the quality of provision.
"The new 30-hour offer is not adequately resourced, meaning money will be spread more thinly."
The Sutton Trust is also calling on the government to review the impact of the 30-hour offer on the school readiness of children from non-working families.
Neil Leitch, chief executive of the Pre-school Learning Alliance, backed the Sutton Trust's call for further investment in professional training.
But he said that while investing in a highly qualified workforce, as the report recommends, is one piece of the puzzle, "qualifications in and of themselves are no guarantee of quality".
"There are plenty of early years practitioners who may not have formal qualifications, but are experienced, passionate, caring and have an excellent understanding of child development," he added.
Purnima Tanuku, chief executive of the National Day Nurseries Association said the effect of the 30-hour offer on school readiness "is a big cause for concern".
"NDNA cautioned the government against rushing out this policy across England without having the time to carefully analyse the pilot schemes and learn vital lessons from them," she said.
The Department for Education has been contacted for comment.