The Government is planning to end the Small Business Grants Fund, Retail, Hospitality and Leisure Business Grants Fund and the Discretionary Grants Fund on August 28.
But the Local Government Association estimates there could be a total underspend of £1.37 billion when the schemes close.
It is urging Ministers to keep the DGF scheme open so councils can try and redistribute any unspent resources from the other two funds back to local authorities to reinvest in supporting businesses.
The LGA said councils have distributed almost £11 billion to almost 880,000 eligible small businesses through the Small Business Grants Fund and Retail, Hospitality and Leisure Business Grants Fund since March.
Cllr Richard Watts, Chair of the LGA’s Resources Board, said: “Councils have given out almost £11 billion in cash grants to businesses and worked hard to set up discretionary schemes to help support as many more as possible.
“It was a huge task to set up these schemes from scratch and the funding has been a lifeline to struggling businesses worried about the future.
“Shutting the discretionary scheme would be a mistake by the Government at this time. Councils need more time and flexibility to ensure as many businesses can benefit from this funding.
“The Government also needs to commit to redistributing any unspent resources from the original schemes, including any clawed back, to councils to be spent on local efforts to help further support businesses and reboot local economies.”
Tej Parikh, Chief Economist at the Institute of Directors, said: “For many small businesses, the fight is far from over. It would be deeply disappointing if this support was withdrawn before time.
“Demand for the discretionary fund shows that many businesses have fallen through the cracks of the main schemes.
“With reopening and adjustment costs ahead, money will be tight for small businesses. Councils have been working to get the money to the front line and should be given the resources to kickstart local business recoveries across the country.”