Households in England face further council tax rises from April, according to research.
The County Councils Network said the majority of councils that run social care services would be raising council tax by the full amount allowed - 3.99%.
But it said councils faced a funding shortfall of £19bn over the next five years and it has called for more cash.
The government said councils would have access to £49.2bn next year, including £1.5bn for social care.
New Chancellor Rishi Sunak will set out the Budget on 11 March.
Labour said the situation showed Prime Minister Boris Johnson's promise to "level up" the country was "worthless".
The County Councils Network, which represents a group of larger local authorities, said 133 councils out of 151 social care authorities have published their draft budgets, which will be ratified next month.
It said its analysis shows that all 133 councils are planning to increase council tax.
All but two of these are proposing to include a 2% social care precept, ring fenced for care services, it said. A total of 116 councils are planning to raise council tax by the maximum 3.99%, according to the research.
The County Councils Network said that the council tax rises would amount to an average increase of up to £69 per household.
But it said that increasing rates would not prevent further cuts to local services run by councils.
David Williams, County Councils Network chairman, said the financial forecasts for the next five years "make tough reading for councils and taxpayers alike".
"This is why the government must use the March Budget to signal that councils will receive a further cash injection in the Spending Review," he said.
He said that with the predicted shortfall, "local politicians will need to continue to make really tough decisions to meet rising demand for services".
Labour's shadow local government secretary Andrew Gwynne said: "Boris Johnson's promise to 'level up' our communities has been shown to be worthless.
"A decade of cuts has devastated local government services - but instead of providing the funding that is needed, this administration has continued to shift the burden onto struggling families.
"If we continue to fund social care like this, it will lurch from crisis to crisis, and we urgently need to see a long-term solution from the government to fix this crisis."
But the Ministry of Housing, Communities and Local Government said the £49.2bn funding it was providing councils in 2020-21 was "the biggest annual real-terms increase in spending power in a decade".
"The funding plans provide certainty for councils who are responsible for delivering the services their communities need and will give local residents the final say on council tax increases," it said.
The County Councils Network represents 36 county authorities in England and is part of the the Local Government Association.