Local services face £1.3 billion in extra cuts, councillors have said.
The main grant funding from central government will be reduced by 36% in 2019-2020, according to local authorities.
And 168 councils will not get any of the grant money at all, the Local Government Association (LGA) said.
In the decade to 2020, councils will have lost 60% of grants provided for services, according to the LGA, which represents authorities across England and Wales.
The financial viability of some councils is under threat, while others are increasingly unable to protect children and provide dignified care for the elderly and disabled, the LGA said.
Council chiefs have called on Chancellor Philip Hammond (pictured) to address the situation in his Budget on October 29.
As part of its Budget submissions, the LGA said that a modelling programme showed residents living in a council area which sits in the mid-range in relation to current funding, levels of deprivation and outlook for economic growth, should expect to see key services "dramatically" cut in the next financial year.
According to LGA figures, funding cuts and inflation would see such a local authority lose £50.7 million in 2019-1920.
That amount of money is equivalent to paying for more than one million hours of home care provision, more than 12,500 weeks of care for the elderly, at least three average sized libraries being kept open, and more than 130,000 pot holes being filled.
Chairman of the LGA's resources board, Richard Watts, said: "Unprecedented funding pressures and demand for adult and children's social care and homelessness services is pushing councils to the limit.
"As a result less money is being spent on the other services that keep our communities running, such as libraries, local roads, early intervention and local welfare support.
"Losing a further £1.3 billion of central government funding at this time is going to tip many councils over the edge.
"Many local authorities will reach the point where they only have the funds to provide statutory responsibilities and it will be our local communities and economies who will suffer the consequences.
"In his spring statement in March, the Chancellor said he would invest in public services if public finances improve as recent forecasts have suggested.
"It is therefore vital that the Government addresses the growing funding gaps facing councils in 2019-2020 in the autumn Budget.
"If the Government fails to adequately fund local government there is a real risk to the future financial viability of some services and councils.
"Investing in local government is good for the nation's prosperity, economic growth and for the health and well-being of our nation.
"It will boost economic growth, reduce demand for services and save money for the taxpayer and other parts of the public sector."
Copyright (c) Press Association Ltd. 2018, All Rights Reserved. Picture (c) Brian Lawless / PA Wire.