Councils are urging Chancellor Philip Hammond to use this month's Budget to stabilise the "perilously fragile" situation in social care.
An extra £1.3 billion is needed from the Treasury to plug funding gaps over the next financial year, the Local Government Association (LGA) have warned.
Councillor Claire Kober, chair of the LGA's resources board, has warned that there is "real and growing uncertainty" about how local services are going to be funded beyond 2020.
She said: "Local government in England faces a £5.8 billion funding gap by 2020. Even if councils stopped filling potholes, maintaining parks and open spaces, closed all children's centres, libraries, museums, leisure centres, turned off every street light and shut all discretionary bus routes they still would not have saved enough money to plug this gap in just two years.
"An extra £1.3 billion is also needed right now just to stabilise the perilously fragile care provider market."
New analysis by the LGA, published ahead of the Autumn Budget, has revealed that by 2020 56p in every £1 of council tax will be spent on caring for the elderly, vulnerable adults and children.
In addition to the surge in social care costs, almost half of councils in England will no longer receive any core central government funding in the form of the Revenue Support Grant by 2019/20.
As part of its Autumn Budget submission, the LGA said local government must first and foremost be allowed to keep all of the business rates it collects locally each year to plug growing funding gaps.
Ms Kober said the Government must recognise that councils "cannot continue" without sufficient resources.
She said: "Demand for services caring for adults and children continues to rise but core funding from central government to councils continues to go down. This means councils have no choice but to squeeze budgets from other services, such as roads, street lighting and bus services to cope."
"Within two years, more than half of the council tax everyone pays may have to be spent on adult social care and children's services. Councils will be asking people to pay similar levels of council tax while at the same time, warning communities that the quality and quantity of services they enjoy could drop."
She went on: "The Government must recognise that councils cannot continue without sufficient and sustainable resources. Local government must be able to keep every penny of taxation raised locally to plug funding gaps and pay for the vital local services our communities rely on.
"With the right funding and powers, local government can play a vital role in supporting central government to deliver its ambitions for everyone in our country."