The Local Government Association (LGA) said its members were already facing £10 billion of cost pressures over the next five years due to national policies, increased demand and inflation.
The body estimates that moves such as introducing the new national living wage for over-25s will cost councils an extra £834 million a year by 2019-20, while there will be one-off bills such as £1.75 billion for business rate appeals after the 2017 revaluation.
The LGA, which represents more than 370 town halls in England and Wales, urged the Chancellor to bear the issues in mind when finalising the Spending Review.
Chairman Gary Porter said: "Our new analysis shows the significant spending pressures facing councils over the next few years even before the possibility of further funding reductions.
"Leaving councils to pick up the bill for new national policies while being handed further spending reductions cannot be an option.
"Enormous pressure will be heaped on already stretched local services if the Government fails to fully assess the impact of these unfunded cost burdens when making its spending decisions for the next five years.
"Vital services, such as caring for the elderly, protecting children, collecting bins, filling potholes and maintaining our parks and green spaces, will simply struggle to continue at current levels."
A Treasury spokeswoman said: "As the Chancellor has said, the forthcoming Spending Review is the next step in the Government's plan to eliminate the deficit, run a surplus and ensure Britain lives within its means.
"While councils have worked hard over the past five years to deliver a better deal for local taxpayers, like the rest of the public sector they will have to continue playing their part in fixing the public finances, to ensure we deliver economic security for working people across the country.
"The Government is clear - we'll deliver more with less and can achieve this while maintaining the public services people rely on, because we've done it before."
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