Councils in England face cuts of £3.3 billion in central government funding next year, a new study has found.
The Local Government Association warned that councils will have to make "significant" savings on top of previous spending cuts.
Funding will continue to be reduced - by 11% in 2017/18 and 4% in 2018/19 before increasing by 7% in 2019/20, said the LGA.
The cuts will leave English authorities facing an estimated funding gap of of £9.5 billion by the end of the decade.
David Sparks, who chairs the LGA, said: "Core local government funding has been protected from further in-year cuts in the Budget but it is clear the Spending Review in the autumn will see councils continue to face challenging funding reductions and spending pressures over the next few years.
"Councils have already made £20 billion in savings since 2010 following reductions in government funding of 40% and have worked hard to shield residents from the impact of funding cuts.
"There are no efficiencies left to be made for many councils while many now warn efficiencies alone will not be enough to cope with further funding cuts. Vital services, such as caring for the elderly, protecting children, collecting bins and filling potholes, will struggle to continue at current levels.
"If our public services are to survive the next years, we urgently need a radical shift in how public money is raised and spent, combined with proper devolution of decision-making over transport, housing, skills and social care to local areas.
"Fairer funding for local services, and the freedom to pay for them, will allow councils to tackle the big issues facing their residents and protect services which bind our communities together and protect our most vulnerable."
Local Government Minister Marcus Jones said: "These unsubstantiated and premature claims are based on funding decisions which have yet to be made let alone announced.
"Councils have worked hard over the past five years to deliver a better deal for local taxpayers, however, like the rest of the public sector will have to continue playing their part in tackling the deficit to ensure the economic recovery continues.
"In the run up to the Spending Review and next local government settlement we will continue to listen to the views of councils, Local Government Association and others about the best way of distributing funding to achieve fairness, efficiency and local growth."