Councils in England are facing a £1.1bn shortfall this year, on top of "almost unendurable" cuts since 2010, the Association of Directors of Adult Social Services has warned.
Freezing care provider fees to save money was no long sustainable, it said.
Ministers say extra money will help NHS and social care services work together.
The survey, which was completed by 147 directors of adult social services for councils in England, suggests that funding reductions to social care budgets have totalled £4.6bn since 2010 - a 31% overall reduction.
Budgets for adult social care - which provides practical support to people due to illness, disability, old age or a low income - will reduce by a further £500m in cash terms this year, it said.
"Taking the growth in numbers of older and disabled people into account, this means that an additional £1.1bn would be needed to provide the same level of service as last year," the report warned.
It said some councils had made savings in the past by freezing fees paid to providers, but care providers were now also facing financial problems.
Some companies - particularly those in southern England - are struggling to attract staff, amid increasing concern about the quality of care, it said.
"What is at stake is the continuing capacity of adult social care to sustain services to those in greatest need," ADASS president Ray James said.
"In virtually all our authorities, the number in need is growing, while the complexity of their needs is increasing."
ADASS called for the government to "protect essential care and support services to the most vulnerable members of our community".
But a government spokesman said the survey "ignores" a commitment to invest £10bn in health services that are being "joined up" with social care, by 2020.
The BBC has launched an online guide to the care system for the over-65s. The "care calculator" covers residential care and the support provided in people's own homes, for tasks such as washing and dressing.
Users can submit their postcode and find out how much each service costs where they live in the UK.
There is also a dedicated BBC Cost of Care website, with news stories, analysis and video.
The spokesman said: "Increasing budgets isn't the only solution. By working innovatively and joining up health and social care we can improve care and also save money."
However, Councillor Izzi Seccombe, from the Local Government Association (LGA), said adult social care services were facing "enormous pressures" due to "insufficient funding, growing demand and escalating costs".
"We have long warned that investing in the NHS whilst social care budgets are under continual pressure is simply a false economy.
"It is social care services that support elderly and vulnerable people to maintain their independence, live in their own community and stay out of hospital longer," she added.
Caroline Abrahams, charity director at Age UK, said the idea of a further £1bn coming out of social care budgets was "chilling".
Sue Brown, vice chairman of the Care and Support Alliance - which represents 80 leading charities - said the figures "confirm what we already know - that the care system is in worsening crisis".
She said "chronic underfunding" of adult social care had seen "dramatic year-on-year rationing of support, excluding hundreds of thousands of older and disabled people from the care they desperately need".
Janet Morrison, chief executive of the charity Independent Age, said: "This worrying survey shows how the frail and elderly in our society are being hit by year on year cutbacks to council services."
"It's vital now more than ever that we have an honest debate about the true costs of providing social care, not just health care," she added.
Adult social care firms are struggling to hire, retain and train staff as a result of cuts to council budgets, a survey of senior officials suggests.