Infrastructure projects, including new roads and bridges, could be at risk unless the government releases billions of pounds of EU regeneration funding.
The Local Government Association (LGA), which represents councils in England, is seeking urgent guarantees from the government that local areas will receive every penny of EU funding they are expecting by the end of the decade.
Local areas in England have been allocated a share of £5.3 billion worth of EU regeneration funding up to 2020. To access the money, each area has put forward innovative proposals, for example to create jobs or build new infrastructure, and it is up to the government to decide which projects the money can be spent on.
The LGA estimates that billions of this EU funding has yet to be released to local areas. For example, Cornwall and the North-east have both only received 20% of their EU funding allocations so far and Birmingham has only received 25%.
Councils are concerned that Whitehall could hold onto EU funding not already diverted to local areas amid the economic uncertainty caused by the vote to leave the EU.
Local government leaders warn any loss of EU funding would be a severe blow to communities across the country.
It could lead to hard-pressed businesses and residents most in need of support losing out on vital projects, such as employment, apprenticeship and skills schemes and tourism-boosting initiatives.
Lord Porter, LGA chairman, said: "Communities and local economies have become increasingly reliant on what EU funds can achieve for them. Councils have used EU funds to help new businesses start up, create thousands of new jobs, roll out broadband and build new roads and bridges.
"Losing any of this vital money over the next few years would be a real blow for local economic growth and communities.
"It is important for the government to end the current uncertainty and guarantee that local areas will receive all of the EU funding they have been allocated by 2020, regardless of whether decisions over which projects it should be spent on have been made or not.
"This is essential to avoid essential growth-boosting projects stalling and local economies across England being stifled.
"An urgent government commitment to protect all of this funding is imperative so local areas can get on with the vital task of creating jobs, building infrastructure and boosting growth."