Just over one in 10 adults over 55 have set aside money to cover the costs of any future care needs, the consumer rights group Which? has warned.
A survey commissioned by the organisation found only 12% were saving in case they needed to pay for care in later years.
In contrast, more than half - 55% - said their priority was spending on things they wanted or needed to do at present.
Which? said the findings suggested any proposals in the Government's forthcoming social care green paper which placed the burden on people to plan themselves for their future needs may be doomed to failure.
Alex Hayman, the group's managing director of public markets, said: "The broken social care system cannot continue to fail older people and their families in delivering high-quality, affordable care when they most need support.
"The Government must recognise that most people won't have made extensive plans for their care, so the system must be designed to help people get the support they need at a time of crisis and stress for themselves and their loved ones."
The Local Government Association said the survey underlined the need for ministers to address a £3.5 billion "funding gap" by 2025, just to maintain existing care provision.
"Adult social care is at breaking point due to years of underfunding, rising demand and costs for care and support," it said in a statement.
"Anyone may need social care and support at any stage of their lives, particularly as we grow older, but a lack of certainty of future funding of adult social care and the split of responsibilities between individuals and councils in who pays for it, is making this hard to financially plan for."
The findings come as the Conservative chair of the Commons Health and Social Care Committee Dr Sarah Wollaston dismissed reported plans for a "Care Isa" to encourage people to save more for social care.
The Sunday Telegraph said ministers were considering the saving scheme - exempt from inheritance tax - for inclusion in the green paper, which is expected before the end of the year.
Under the proposal, the Isa would be capped to reflect care costs and any money left over at death would be passed on to the holder's family without being taxed.
However Dr Wollaston wrote on Twitter: "This won't solve the care crisis at all. There is no pooling of risk.
"It only 'solves' it for a small minority of wealthy people who can afford to invest and whose families benefit from paying lower tax on their inheritance if not used for care."
A Department of Health and Social Care spokeswoman said: "We have provided local authorities with access to £9.4 billion in dedicated social care funding over the last three years.
"Our green paper due in the autumn will set out our plans to reform the social care system to ensure it is sustainable for the future."
Populus, on behalf of Which?, surveyed 2,104 UK adults, of whom 793 were aged 55 and over, online between 11 and 12 June.
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