Town hall officials fear they will not be able to plug the hole in funding for council tax benefit left by Government cuts.
Research found 86% of councils cannot meet the 10% grant reduction through back office savings, fuelling concerns the payments, which support the poor and vulnerable, will be reduced or axed altogether in many parts of the country.
Senior local authority managers also want to be free to raise council tax bills next year, according to the study by the Local Government Information Unit (LGiU) and The Municipal Journal.
Around 95% of executives support another round of Government-backed freezes on the levy in the new financial year but 80% want more control over local rates in 2013.
Senior managerial staff, such as chief executives and chief finance officers, in 81 English local authorities responded to the study.
Andy Sawford, LGiU chief executive, said: "There is some good news for government here, with most freezing council tax, and a small majority expecting changes to business rates to benefit their council.
"However, there may be trouble ahead as councils predict significant inflationary pressures and want the flexibility to increase council tax in future years. The major concern both in the medium and long term is the effect of demographic change on demand for older people's services. This confirms the importance of the Government bringing forward proposals for changes to social care funding in the forthcoming White Paper."
A Department for Communities and Local Government spokesman said: "Every bit of the public sector needs to help pay off the budget deficit.
"Councils have delivered significant efficiencies. 'Can do' councils are working together to innovate, do things differently, reform and rethink services around resident needs, reducing duplication and driving out waste. But there is still more that can be done.
"Councils need to carry on doing everything in their power to improve their productivity and seek out new and innovative ways of delivering services through: smarter procurement, reducing the costs of management and support services, sharing services, reducing building costs and assets."