Its annual Future funding outlook said in 2016/17 councils would need to find savings equivalent to 12% of their total budgets.
The LGA also predicted that the upcoming Spending Review would see Whitehall funding reduced by a further 11% in 2017/18 and 4% in 2018/19, before increasing by 7% the following year.
This means councils face a funding gap of £9.5bn by the end of the decade, the outlook claims.
Spending on social care and waste collection will continue to absorb a rising proportion of council resources, the association said, while funding for other local authority services will continue its downward spiral by 35% in cash terms by the end of the decade, from £26.6bn in 2010/11 to £17.2bn in 2019/20.
The LGA called for “radical reform” of the way public services are paid for and delivered. At its annual conference, the association it will issue a report setting out detailed Spending Review proposals to ensure local services survive over the next few years.
LGA chair David Sparks said: “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.
“There are no further 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.”
But local government minister Marcus Jones called the LGA's claims "unsubstantiated and premature". He said they were based on funding decisions that had 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," Jones said.
“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.”
