The government should greatly expand family centres under the Sure Start brand to help win back Reform voters in former Labour heartlands, a commission backed by Labour politicians has said.

Hilary Armstrong, the Labour peer and former cabinet minister, was among those pressing for a fuller reintroduction of family centres under the Sure Start label, saying it would help to rebuild trust in neighbourhoods damaged by austerity.

Armstrong is chair of the Independent Commission on Neighbourhoods, which said its polling showed 62% of people recognised the Sure Start brand, and that 76% would like to see it revived.

Bridget Phillipson, the education secretary, announced last month that one-stop-shop family hubs similar to Sure Start would be introduced throughout England to give parents advice and support.

The £500m project will open up to 1,000 centres from April 2026, meaning every council in England will have a family hub by 2028. It will be called Best Start and will build on the existing family hubs and the start for life programme to provide a single point of access for services in health, education and wellbeing services.

The policy forms part of the government’s push to replace services lost since 2010, which include the closure of more than 1,400 Sure Start centres.

At their peak under Gordon Brown, there were more than 3,600 Sure Start centres, which were considered one of the previous Labour government’s biggest achievements.

Government sources said the Best Start brand was tested and came out as the clear winner against other options, with focus groups drawn from expectant parents up to those with 10-year-olds, all participants from lower socioeconomic groups. Parents in the groups opted for Best Start as the clearest description of intent, who it was aimed at and a sense of parents’ ambitions.

The hubs are intended to be a bigger umbrella for services than Sure Start, ultimately encompassing Labour’s wider offer, from free breakfast clubs to school-based nurseries.

However, the Independent Commission on Neighbourhoods said the policy should be returned to its original Sure Start name to have the maximum impact.

Jo White, a Labour MP who chairs the “red wall” grouping in parliament, said: “Labour’s reconnection with left-behind communities, including in the ‘red wall’ constituencies, has to be tangible. People need to see and experience change, and the reopening of Sure Start centres is a very good start.”

Hilary Armstrong said: “On our visits across the country we have heard time and again how Sure Start made a positive difference to the lives of people in ways that few other policy initiatives have done. Our work has shown that bringing back Sure Start centres through upgrading existing services in the most disadvantaged places would not only be good value for money but would also start to rebuild trust in neighbourhoods which saw services taken away due to austerity.”

Polling by ICON found reinstatement as Sure Start would have cross-party appeal, including to working-class voters who switched to Reform in May’s local government elections and whose continued support for Nigel Farage’s party threatens scores of Labour seats. It found 65% of Reform voters said they backed its return, along with 82% of Liberal Democrat voters and 87% of Green voters. Among those described as “Reform curious” – voters open to backing the party – support rose to 68%.

The polling found that Sure Start was more commonly identified with the Labour party than with the Conservatives or coalition, and that 61% identified children as beneficiaries, 56% poorer families and 39% working-class people. Of those questioned, half said the return of the programme would make them view the government more favourably, while a third said it would make them more likely to vote Labour.

Ministers are understood to want to honour the legacy of Sure Start while embedding the Best Start hubs even deeper into the system to make sure they cannot be easily dismantled by future governments.

A Department for Education spokesperson said: “Giving children growing up in our country the best start in life is central to our mission to break the unfair link between background and success.

“This government is revitalising family services, rolling out up to 1,000 Best Start family hubs in every local area, relieving pressure on parents and building on the successful legacy of Sure Start.

“Through our Plan for Change, our Best Start services will deliver 30 hours of government-funded childcare, expand school-based nurseries, and roll out free breakfast clubs in every primary school to support working parents.”