Sure Start children’s centres delivered major health benefits for youngsters in the most deprived areas, reducing the number of people taken to hospital and delivering millions of pounds in savings to the NHS, a study has found.

The Institute for Fiscal Studies research found that where Sure Start offered high levels of service in poor neighbourhoods in England, visits to hospital to treat injuries fell among all children of primary school age, and by a third of all 11-year-olds.

The study questioned the current cuts to children’s centre budgets – reduced by two-thirds nationally between 2011 and 2017 – and urged the government to acknowledge Sure Start’s “big positive effect on children’s health” in future public spending plans.

It also highlighted its effect in reducing health inequalities. “Since the benefits are biggest in the poorest neighbourhoods, access to Sure Start can help close around half the gap in hospitalisations between rich and poor areas,” said Gabriella Conti, a UCL academic and the study’s co-author.

The study argues that because returning funding levels to the 2009 peak may be difficult, new investment should be focused on providing Sure Start services in neighbourhoods with the highest levels of child poverty, on the grounds that they would be more likely to benefit from them.

There was also evidence the programme delivered significant financial savings to the NHS. Direct savings through fewer hospital visits saved £5m, or about 0.4% of annual Sure Start spending. When the lifetime health savings of avoiding childhood injuries were factored in, the level of savings reached 6% of the Sure Start budget.

The study found no evidence that Sure Start helped reduce child obesity among five-year-olds or improved maternal mental health, although it added that data limitations should not be taken as evidence that there was no effect in reality.

Tracy Brabin, the shadow early years minister, said: “This research shows the critical role Sure Start plays in children’s health, as well as their development.

“But shamefully, over a thousand Sure Start centres have been lost through years of austerity, meaning children and families across the country are missing out.”

Poverty expert Naomi Eisenstadt, who was the first director of the government’s Sure Start unit in 1999, welcomed what she called an authoritative piece of research, and urged ministers to start to reverse early years spending cuts. “I hope this study changes the conversation of Sure Start,” she said.

A key objective of Sure Start was to provide specialist heath services to parents, such as baby-weighing clinics, alongside more general health advice and parenting support, childcare and employment advice. Up to now proponents have struggled to back up public support for the policy with clear evidence of its effectiveness.

Sure Start was a flagship New Labour policy and the first centres were set up in deprived areas. In 2004 the programme was expanded with the aim of delivering “a children’s centre in every community”. At its peak in 2009-10, Sure Start had 3,600 centres and a £1.8bn budget, before austerity cuts introduced by the coalition reduced centre numbers by up to 1,000, and funding by two-thirds.

A Sutton Trust-funded study published last year criticised “piecemeal” cuts to Sure Start centres and said that a fifth of English local authorities planned to reduce the number of children’s centres in the future as reductions in central funding forced them to draw up “bare legal minimum” levels of services.

Cllr Anntoinette Bramble, chair of the Local Government Association’s children and young people board, said: “It is inevitable that without new investment from government in children’s services, councils will face the difficult but unavoidable decision of having to cut or close early help services such as children’s centres.”

The study tracked the impact of the programme on children of primary school age during the first 10 years of Sure Start, from its inception in 1999 to the high point of its coverage in 2009.

A Department for Education spokesperson said: “Children’s centres can play an important role in supporting families, and local councils decide how to organise and provide services for families in their areas to meet local needs – whether this is through children’s centre buildings or delivering services in different ways, and we continuously reflect on what works best.

“We want every child to have the best start in life, which is why our ‘healthy child programme’ means children and families receive five mandatory health visitor checks before they are two-and-a-half.”