Brexit is putting at risk a £5bn “lifeline” of EU regional cash for important social, employment and infrastructure funds because the government has yet to come up with a plan for replacement money, local council leaders have warned.

They said that with national funding being depleted councils in England have become “increasingly reliant on EU money”, with local leaders desperate to get a decision on whether or not there will be replacement funding when the current round of finance runs out at the end of 2020.

The government announced a year ago that it intended to consult on the design of the domestic replacement fund by the end of 2018.

“This still has not happened,” said the Local Government Association (LGA) which called it a “huge concern”.

Much of Philip Hammond’s £26bn fiscal headroom has already being promised on big-ticket items such as extra police and tax cuts by both Tory leader hopefuls Jeremy Hunt and Boris Johnson, and councils fear they would be the ones to lose out in any settlement post-Brexit.

Kevin Bentley, the LGA’s Brexit taskforce chair, said: “Brexit cannot leave local areas facing huge financial uncertainty as a result of lost regional aid. This funding has been used by local areas to create jobs, support small and medium enterprises, deliver skills training, and invest in critical transport and digital infrastructure and boost inclusive growth across the country.”

The money comes from the European social fund, the European regional development fund (ERDF) and the European agricultural fund for rural development. The funds have helped improve roads, bring broadband to rural communities, train people with disabilities to help them get into work, as well as providing funds for tourist and environmentally important sites.

In Portsmouth and Southampton the programme supports the long-term unemployed and people with disabilities and health conditions that make work challenging.

In many cities, ERDF allocations have provided match-funding to help small businesses get off the ground.

A citywide enterprise programme in Leeds involving pre-startups and businesses under three years old is one of the largest beneficiaries, with a total of £9.1m in match-funding to the local authority and Prince’s Trust contribution.

Bentley said: “With 18 months until funding runs out, the government needs to work urgently with councils to develop a fully funded and locally driven successor scheme. With national funding for regeneration increasingly being depleted, all local areas have become increasingly reliant on EU money, and local areas are desperate to get on with creating jobs, building infrastructure and boosting growth.”

A Ministry of Housing, Communities and Local Government spokeswoman said: “We know the importance of local growth funding to local places and of providing certainty on their future. That’s why we are talking to interested parties on the design of the UK shared prosperity fund to ensure it can support those parts of our country whose economies are furthest behind.”