The government is being urged to install trade union members on the board of its new £7.3bn national wealth fund to help offset the influence of big banks and ensure that it is geared towards hitting green targets and bringing “shared prosperity” to the UK population.

It is part of a wider set of recommendations set out by the campaign group Positive Money, aimed at shaping the governance and investment plans of the national wealth fund (NWF), which was launched by the chancellor, Rachel Reeves, after the July election.

The NWF is part of government efforts to attract billions of pounds of private-sector cash – roughly £3 for every £1 of taxpayer cash – for big infrastructure projects across the UK, including ports, gigafactories and hydrogen and steel projects. The government is hoping that putting £7.3bn of public money forward will persuade private funders to put their own money on the line.

While the government has yet to release further details of how the NWF will be run, Positive Money is concerned that the blueprint will be disproportionately influenced by City bosses.

Labour has so far relied on a taskforce made up of the chief executives of firms including insurer Aviva and banks such as NatWest and Barclays, as well as the former Bank of England governor Mark Carney.

The group said the fund should “focus on delivering for workers and communities, not just investors”, and be governed by an independent board and investment committee with “strong representation from civil society” – potentially including thinktanks such as the IPPR and climate strategists E3G – “and, in particular, trade unions, to help ensure the NWF supports a genuinely just green transition and shared prosperity”.

It added: “These recommendations arise from what Positive Money sees as over-representation of the financial industry in the national wealth fund taskforce.”

The launch of the new wealth fund quickly followed Labour’s controversial decision to cut its £28bn green investment pledge in half – a move that prompted an angry response from green groups, unions and others.

Positive Money said the NWF should aim to operate more like the much revered £580bn KfW development bank in Germany, but it would have to grow to more than £460bn to reach the same per-capita scale as its European counterpart.

It said this could be done in part by giving the NWF powers to raise money by issuing bonds through financial markets, and have its borrowing be excluded from government fiscal rules that cap public sector debts, giving it more freedom to borrow and invest at scale.

The campaign group said the NWF should devolve investment decisions to a network of 12 “regional banks” based in Scotland, Wales and Northern Ireland plus the nine regions of England, which would seek guidance from local authorities, as well as local industry and businesses, about how to allocate funds. Decentralising investment decisions would “ensure funds are best channelled to where they are needed across the whole country”.

Simon Youel, head of policy and advocacy at Positive Money and author of the research, said Labour had an opportunity with the NWF “to establish a long-lasting, legacy public institution”.

“The NWF isn’t just an opportunity to deliver social and environmental value to the public after years of underinvestment. It’s a chance for the public to finally start seeing some returns on their investment, instead of the ‘privatised rewards, publicised risk’ model that has become all too familiar in recent decades,” he said.

“With genuinely ambitious mandates, objectives and financing power, the NWF could join the ranks of purpose-driven public banks the world over, and demonstrate the potential of public finance to deliver truly transformative change, such as the rapid and just decarbonisation of our economy and infrastructure.”

A Treasury spokesperson said: “The national wealth fund will play an important role in the government’s industrial strategy and growth and clean energy missions, making transformative investments across every part of the country, supporting thousands of good jobs and making everyone better off, while generating a return for the taxpayer.”

The spokesperson added that further details would be set out in due course.