The Local Government Association (LGA) has warned local councils face a £2.6 billion shortfall in funding for social services by 2020.
Analysis by the LGA has estimated 57 social care authorities will be worse off in 2016/2017.
Overall two-thirds of councils will see their funding cut, with a total funding gap of £5.8bn by 2020.
Hull is likely to be one of those authorities.
The Governments response to the crisis has been has been to allow authorities to raise Council tax to cover the gap.
However, in 2016 The Kings Fund identified Hull as being one of five authorities likely to generate the lowest increases in income if the precept were increased.
Lib Dem Councillor Claire Thomas commented: “Local councils, such as Hull, are being gradually starved of cash under this government, with a devastating impact on social care.
“A rise in Council Tax will hit the poorest in our society the hardest and simply not cover the social care funding gap in a place like Hull.
“The sad reality is without more investment in local authorities and our health service, those who rely on care will not be treated with the dignity they deserve.
"Only the Liberal Democrats are prepared to make the case that we may need to raise tax to secure the future of our NHS and social care."