A study by the Institute for Fiscal Studies (IFS) showed that in areas with the best access to children's centres - measured as one centre per 1,000 children aged 0-4 - there were 5,500 fewer hospital admissions per year compared with pre-Sure Start levels.
This represented a reduction of 18 per cent on levels recorded before Sure Start was introduced 20 years ago.
The IFS research suggests that the benefits of children's centres are greatest among children living in disadvantaged areas - no effect was found on hospital admission rates in the richest 30 per cent of neighbourhoods.
The findings mean that providing access to Sure Start at 2010 levels closes the gap in hospitalisation rates between the 30 per cent poorest and richest areas by around a half at the end of primary school.
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The drop resulted from parenting advice - including guidance on keeping children safe and improving their behaviour - and health education.
The study suggests that the reductions were more likely to be for infection related reasons in younger children, while accidents and injuries were behind the drop for older children.
Sure Start was introduced by Tony Blair's first Labour government, initially to serve disadvantaged neighbourhoods, before later being rolled out across England to provide health, education and childcare services.
Council spending on children's centres peaked at £1.8bn a year in 2010 but has been cut by two-thirds since then, and between 2011 and 2017 more than 500 sites have been closed - 170 of which have been in the poorest 30 per cent of neighbourhoods, according to the IFS.
There has been significant variation between councils, with some closing the majority of their centres, while others have kept them open but reduced the services available through them.
Research published in April 2018 by the Sutton Trust, suggested that up to 1,000 children's centres had been closed since 2010.
Children's centre closures have been controversial, and some parents have fought against them, such as in Buckinghamshire, where a judicial review has been launched into plans to close more than half of them.
Neil Leitch, chief executive of the Early Years Alliance, said that the findings would come as no surprise to those who have experience of Sure Start centres.
"What is shocking, however, is the carelessness with which the government has treated these invaluable community assets. Successive ministers now have overseen the mismanaged decline of Sure Start," he said.
"If ministers were ever serious about social mobility then now would be the time to show it. This report makes clear what's at stake and the government should be questioning where their indifference has left some of our most vulnerable children - and start reinvesting in and reaffirming their support for Sure Start immediately."
Antoinette Bramble, chair of the Local Government Association's children and young people board, said it was "inevitable" that without new investment from government in children's services councils will face having to cut or close children's centres.
Rachel Dickinson, president of the Association of Directors of Children's Services, said: "This research clearly shows that children's centres have had major benefits for children's health. Growing demand for services, local needs and tightening council budgets have made it necessary for local authorities to rethink and reshape the way services from children's centres are delivered working with their partners to do this.
"However, there is not enough money in the system to meet the level of need in our communities. We are having to make increasingly tough decisions like cutting early help services that reduce future demand."
IFS research economist Christine Farquharson added: "Sure Start has had a turbulent history, with a fast rollout followed by deep spending cuts. But these decisions were not always based on thorough evidence about the programme's impacts on children and their families.
"Ahead of the Spending Review, it's crucial that both central government and local authorities use the best evidence available to decide on their vision for Sure Start as the programme turns 20. Our findings suggest that limited resources are best focused on the poorest areas."