People could be given tax relief to encourage them to put money aside for their care in old age under a plan to be considered by the Government.

Philip Hammond announced that a green paper on the long-term funding of social care would be published later this year. He ruled out imposing a “death tax” on people’s estates to pay their social care bills when they die but raised the prospect of radical reform for the way care for the elderly is funded.

The Chancellor is believed to be interested in a proposal to urge people to put savings into tax-free “Care ISAs”, which could also attract a government bonus.

The Treasury could allow tax-free withdrawals from pension funds if the money were spent on care. The downside is that many households will see their incomes squeezed for the foreseeable future and will have little spare cash to set aside.

Mr Hammond insisted that a “death tax” had never been on the Government’s agenda. However, it is believed that Downing Street wanted all options to be considered during a review being led by the Cabinet Office. Mr Hammond has now killed off the proposal.

Some Tories believed they would have been accused of hypocrisy if they had revived an idea they branded a “death tax” when the Labour Government put it forward during all-party talks ahead of the 2010 election.

A levy on people’s estates would redistribute wealth. It would pool risks and reduce the unfairness of a system in which half the population spends under £20,000 on care but one in 10 must find more than £100,000.

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However, it would reduce the amount that better off people could hand down to their families when they die.

Ministers admit that the £2bn extra for social care over three years announced in the Budget will provide only a stop-gap solution and that reform is needed because the number of over 75s will rise by two million in the next 10 years.

“Care ISAs” have been championed by Baroness Altmann, the Tory former Pensions Minister. She said: “Taxpayers simply cannot afford to support increasing numbers of elderly people, but the money must come from somewhere.

“Encouraging everyone to save for later life care, which one in four will need (and one in two of many couples), would signal that care costs must be planned for and incentivising such savings is vital in our ageing population.”

Responding to the Budget, Lady Altmann said the extra £2bn for local authority care budgets might not be enough to relieve pressure on the NHS and was “just a sticking plaster on a weeping wound”.

“Care ISAs” could be combined with a lifetime cap on the amount an individual would have to spend on social care, with the rest met by the state. After a review headed by Sir Andrew Dilnot, the Conservatives backed the idea of a £72,000 limit.

It was included in the Tory manifesto at the 2015 election but shelved until 2020 two months after they won power. It could now be revived to stop families running up huge care bills care when an individual has savings of more than £23,500 and does not qualify for state help under the current system.

Other options to be studied by the review include a German-style national care fund, into which employers and workers pay.

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This could be achieved through a rise in national insurance contributions (NICS). But Mr Hammond has already provoked controversy by raising them for the self-employed in the Budget, and so may be wary of going down this route.

Another system is Japan's, in which over-40s must pay into an elderly care insurance system according to incomes and where they live. Over 65s see their premiums deducted from their pensions.

A sensitive option would be to extend NICS to pensioners and use the proceeds for state-funded care.