Sunderland's leaders have welcomed calls for fairer Government funding.
The move has been made by the Local Government Association (LGA) as part of its Autumn Budget Submission, which is highlighting the pressures authorities are under.
The LGA is warning that the money local government has to provide vital day-to-day local services is running out fast.
For every £1 of council tax collected by councils in 2019/20, the LGA forecasts 56p could be spent on caring for the elderly, vulnerable adults and children.
This is up from 41p in 2010/11.
In Sunderland, more than £295 million has been taken out of its budgets in the last eight years because of the Government's austerity programme.
Council Tax raises only 14p for every £1 of city spending.
This year Council Tax increased by nearly five per cent (4.9 %) in Sunderland with three per cent raising an extra £4.2 million to help meet the cost of increasing demand for adult social care.
Councillor Mel Speding, the council's cabinet secretary, said: "Councils across the country are seeing increasing pressures on all their services and how they are delivered.
"Government assistance has not been forthcoming and Government has continued to reduce the core funding that councils receive.
"Now, the LGA is warning there is real and growing uncertainty about how local services are going to be funded beyond 2020.
"Here in Sunderland we are continuing with reviewing all our services and with fewer and fewer resources it is getting more and more difficult."
The chairman of the LGA, Councillor Claire Kober said: "Within two years, more than half of the council tax everyone pays could 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.
"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 billon is also needed right now just to stabilise the perilously fragile care provider market."
Sunderland has already agreed the majority of its cuts for 2018/19.
Further savings will have to be found from more reviews and cost-cutting in the next two years.
The Government will announce its funding for local government for next year in December.
A provisional Sunderland Council Tax figure for the next financial year is due to be announced in February 2018 with the council setting and finalising its next budget in March.