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Over-50s could be forced to pay an extra 1% on top of their National Insurance contributions to fund their own care in later life.
The idea, which could cost older tax-payers at least £300 a year extra, is being proposed by Conservative Damian Green as part of a range of measures to fill a £2.5 billion social care funding gap.
The Ashford MP says richer people could pay into a voluntary insurance policy or release cash from their homes to top-up the level of their care.
His report calls for a new state pensions-style Universal Care Entitlement.
He said: "We need to change social care radically. The state pension is now at an acceptable level so I am suggesting we have a Universal Care Entitlement on which we'd spend more money than the state currently spends on care.
"But just as we have private pensions which millions of people save into, we should encourage people to take out what is effectively an insurance policy which I am calling a Care Supplement so they could guarantee an even better level of care so they can buy complete peace of mind in old age."
But Labour quickly dismissed his plan, outlined in a report for the Centre for Policy Studies, as a tax on ageing.
"Social care is really stretched now and will become more stretched in the future as the population ages..." Damian Green
Shadow Chancellor John McDonnell said: "After nearly a decade of brutal cuts to social care, the Tories now want to make older people pay through increased taxes.
"We want to hear today a clear statement from the government that they will reject this call, protect the triple lock, and follow Labour’s call to fund social care properly.
"Anything less than a clear rejection of these plans to punish older people, and the voters will need to draw their own conclusions."
The row comes ahead of the publication of the Government's long-delayed social care green paper which Mr Green started work on before he was asked to step down from the Cabinet in 2017.
The publication, which was due to be unveiled on April 1 after being first promised in the March 2017 Budget, is now slated only for publication in "due course".
Mr Green, speaking on Sky News, said another £2.5 billion a year was needed to get "everything up to an acceptable level of provision."
He said: "A Care Supplement would guarantee top of the range care in old age if needed.
"That way, people would know that even if they needed very expensive care they would have taken out an insurance policy so they wouldn't put all their inheritance at risk. They would know they would have something to leave for their children."
He added: "For those who can't afford to top-up their care - 20% of people have no property wealth or don't earn very much during their working life - they would still get a better level of care than they get now."
He insisted: "I accept we must spend more money across the board. Social care is really stretched now and will become more stretched in the future as the population ages. We need to bite the bullet and say the amount of money the state puts in needs to go up quite significantly, year after year."
Mr Green said social care should be funded nationally.
He said: "Local authorities should not be responsible for the funding. Over time, over half of council spending will be going on social care. I don't think that is fair on local councils faced with a choice of that or fixing potholes and keeping libraries open. It should be a national tax and not a local funding issue.
"The problem with the current system is that the Government puts in extra money but it is just a series of sticking plasters. We have to recast the system radically.Both major parties have tried to deal with this and both have got into political trouble because of it. I hope this might even get a cross-party consensus."