The government's current funding arrangements will soon result in closure of basic services according to Conservative chair of the Local Government Association (LGA).
He predicts funding cuts combined with rising demand for services will create a funding shortfall of £14.4bn, with only funding remaining for skeletal services such as social care.
The LGA said spending on core services such as adult social care, children's social services and refuse collection, will absorb an ever greater share of council funds, with the effect of reducing funding for other council services by 46%.
This will mean the running down or closure of services such as libraries, school support schemes and youth clubs, and the shortfall is likely to fall hardest on the most deprived areas.
LGA data shows that the 50 most deprived councils in England will have potential funding gaps of up to 48%.
They also predict that local authorities will face legal challenges as they try to balance meeting their statutory duties and delivering a balanced budget, as there are many services that will receive cuts that they also have a legal duty to perform.
Conservative chair of the Local Government Association, Sir Merrick Cockell, said:
It is evident that a system in which demand and costs are going up and funding is going down is unsustainable and unless something changes, by the end of the decade, councils will not be able to deliver existing services in the way they are delivered now.
Eric Pickles, communities secretary, has said at the LGA conference that the solution to this is to create savings from local authorities.
He believes that community budget pilots will create savings by forcing different public services to work together more effectively in local areas. These will be rolled out nationally and Mr Pickles says they have the potential to save billions of pounds.
Peter Fleming, Local Government Association improvement chair, said :
The community budget stuff he mentioned was really positive. Bringing all the public sector budgets of an area together is good, but what we need is a bigger commitment from the government.