Even if council tax revenues increased by 4.5% a year, adult social care spending is likely to amount to half of all revenue from local taxes by 2035, the IFS has predicted.

There is “no easy way to square the circle”, the think-tank recognised in its report Adult social care funding: a local or national responsibility?, “without backtracking on reforms to local government finance and reintroducing general grant funding”.

Grant funding from government is planned to end by 2020, and councils will be expected to rely on council tax and business rates for most of their revenue.

If councils meet their social care costs through local tax revenues “the amount left over for other services – including children’s services, housing, economic development, bin collection – would fall in real terms (by 0.3% a year, on average)”, the IFS warned in the report, funded by the Health Foundation charity.

One in 10 councils are to see their share of the population aged 75 and over increase by 6 percentage points or more over the next 20 years, the IFS noted.

Potential solutions all have drawbacks, the report suggested.

These include a ring-fenced top-up grant from government but this could lead to councils cutting back on how much of their own money is allocated to these services.

If government fully funded social care, this would “remove over one-third of what councils currently spend from local control, reducing residents’ say in local spending decisions”, the report stated.

Polly Simpson, research economist at the IFS, said: “The government has to decide whether it thinks adult social care is ultimately a local responsibility, where councils can offer different levels of service, or a national responsibility with common standards across England.

“If it opts for the latter, it cannot expect a consistent service to be funded by councils’ revenues, which are increasingly linked to local capacity to generate council tax and business rates revenues.”

David Phillips, associate director at IFS, suggested the government could “decide to keep and, over time, increase the general grant funding for councils that it currently plans to abolish in 2020”.

Speaking to an audience of social care workers on Tuesday, the health secretary recognised the “economics of the publicly funded social care market are highly fragile” and said care models needed to “transform and evolve”.

He said: “We will therefore look at how the government can prime innovation in the market, develop the evidence for new models and services, and encourage new models of care provision to expand at scale.”

Hunt outlined seven key principles the government is considering as it draws up its social care green paper, due to be released before the summer.

He added: “We must make sure there is a long-term financially sustainable approach to funding the whole system.”

He added that this would “take time” but “must not be an excuse to put off necessary reforms”.

“Nor must it delay the debate we need to have with the public about where the funding for social care in the future should come from – so the green paper will jump-start that debate,” Hunt promised.

He also said he would look at making paying for social care fairer and less dependent on the “lottery of which illness” a person gets.