The £72,000 limit, from 2016, will benefit just 8% of men and 15% of women, Institute and Faculty of Actuaries (IFoA) analysis says.

It points out the cap covers direct care costs only and people could spend up to £140,000 before they are helped.

Ministers say changing the current “unfair” system will help more people.

The cap was announced in March 2013 in an attempt to deal with some of the costs associated with caring for an ageing population.

Prior to the establishment of the cap, anyone with assets of more than £23,250 would be expected to fund all of their care, whether in their own house or at a residential home.

This led to elderly people routinely being forced to sell their property to pay for their care and led to the setting up of the Dilnot Commission by the coalition government in 2010.

It reported in 2011 and recommended a cap on the lifetime cost of social care to an individual of between £25,000 and £50,000 with the government picking up the bill above the capped level.

The final level of the cap – £72,000 – was announced by Chancellor George Osborne in 2013.

He also said that the capital limit for means-tested care costs would be set at £118,000, which it was hoped would allow more people to keep their homes.

Modelling provided by the government as it launched a consultation on the plans suggested it was likely to benefit one in eight people.

The IFoA report comes after Labour analysis last November also highlighted the extra care home costs that would not count toward the cap.

The IFoA said that because the cap did not cover accommodation and living expenses – but rather the amount a local authority pays for care – an elderly person could have spent £140,000 before qualifying.

And the institute, which is an independent professional body, warned that many people’s pension savings were not enough to cover the cost of elderly care.

‘In for a shock’

It wants ministers to introduce tax breaks so that people would be encouraged to save money to pay for their future care.

It also recommends setting up a specialist Pension Care Fund, which would be subject to the same tax rules as pensions, but used to pay for the cost of a spouse or relative’s care.

One of the report’s authors, Thomas Kenny, said: “Recent research data shows that one in three women and one in four men aged 65 today is likely to need care.

“Yet the average disposable income for retired households was £18,700 in 2011-12, which is below the level required to fund the average long-term care costs before reaching the cap.

“Anyone who is expecting that the cap will pay for care is in for a shock. The cap is there to protect against catastrophic care costs and we estimate that few people entering care aged 85 years will reach it.”

But a Department of Health spokesman said the current system meant people with more than £23,250 “are literally on their own and many have to sell their homes in a time of crisis to pay for the care they need”.

“We are introducing the first ever cap on care which will protect people from catastrophic care costs and deferred payments so no-one should be forced to sell their home in their lifetime to pay for care,” said the spokesman.

“On top of this we have increased the means-testing level so that government help kicks in far earlier than before, meaning two-thirds of people who reach the cap will pay less than £72,000.”