East Sussex County Council is already warning it could be left with a £55m deficit in its budget next year.
Funding cuts have driven the authority to make nearly £140m of savings since 2012, and now even its core offer is under threat, according to a report.
Council leader Keith Glazier said the unsustainable financial position meant service levels would be ‘severely’ affected without government action.
The council’s political group leaders will write to local MPs, urging them to press the Government for immediate financial support and a sustainable long-term funding arrangement for local government.
Leaders will also call for reform of the special educational needs and disabilities system, a long-term national funding settlement for adult social care, and limits on the profits agencies can make providing staff and on children’s residential care.