Conservative cuts to inheritance tax would be scrapped to pay for the 17 per cent hike in Carer's Allowance, the Labour leader will say during a visit to Birmingham.
Weekly payments would rise from £62.70 a week to £73.10, which would bring the rate into line with Jobseeker's Allowance.
His policy drive comes as recent polling on who would be the best prime minister saw him slump to 14 per cent among all voters and also follows criticism by Labour MP Neil Coyle, who said a complaint made about him by the Islington North MP's office was "absurd".
Jeremy Corbyn will announce that "unsung heroes" will be given £10 a week in benefits boost
Britain's social care crisis was made in Downing Street by cutting £4.6 billion from council care budget
Mr Corbyn will say: "Britain's social care crisis was made in Downing Street by cutting £4.6 billion from council care budgets. Millions of unpaid carers have been forced to fill the gap and put under even greater pressure as a result.
"The care they give to the disabled, sick and elderly saves taxpayers £132 billion a year. So we believe these unsung, unpaid heroes not only deserve our praise and recognition – they deserve better financial support.
"That's why Labour is convinced it's both morally and economically right to give the Carer's Allowance a boost of £10 a week.
Neil Coyle said a complaint made about him was "absurd"
"We also think it's only fair that this extra support for carers is funded by scrapping the Tory cut on inheritance tax, which will only benefit the wealthiest people in Britain.
"This will be the first step in helping to transform our social care system for the 21st century and boosting support for family carers."
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Around 6.5 million people provide unpaid care for older, disabled and seriously ill relatives and friends but many of those eligible for welfare support do not claim it, according to Labour.
It found an estimated 795,000 people were receiving Carer's Allowance in August 2016 and the figure is going up by around 50,000 a year.
Claimants have to spend at least 35 hours a week looking after someone and Labour said its reforms would benefit an estimated one million carers by 2021.
It said the projected cost of the policy in 2020/21 would be £538 million, which would be covered by the expected cost of the £650 million cut to inheritance tax, which allows married couples to pass on estates worth £1 million free of death duties, it plans to reverse.
According to Labour, around 6.5 million people provide unpaid care for older or disabled relatives
Shadow care minister Barbara Keeley will say: "Unpaid carers play a vital role in our society and that role is too often ignored. There are an estimated 6.5 million unpaid carers in Britain providing care and support for family members and friends
"Our health and care system would not manage without the care that they provide. Without them, millions of people would have to manage without any support at all.
"Labour believes that we should find ways to improve support to people who themselves give so much unpaid support to family members and friends.
Jeremy Corbyn in pictures Tue, July 12, 2016
Labour Leader Jeremy Corbyn takes part in a community meeting at the Guru Har Rai Gurdwara Sahib temple
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Britain's opposition Labour Party leader Jeremy Corbyn speaks at an anti-racism rally in London
"This small increment, funded by reversing a Tory tax cut for the rich, is the first step on the road to creating a care and support system fit for all those who need it. It will go some way to alleviate the financial burden that many family carers experience."
Tories claimed Labour would be unable to fund the promise to increase the allowance.
Luke Hall, a member of the Work and Pensions Select Committee, said: "Carers make a huge contribution to society, so it's only right that we do everything we can to support the selfless work they do.
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Tories claim Labour would be unable to fund the promise to increase the allowance
"That's why we already increased the rate of Carer's Allowance, meaning an additional £450 a year for carers since 2010.
"Labour have already committed the money from corporation tax cuts 11 times over, so there is no way they could find the additional money for this promise.
"It's not worth the paper it's written on – just like Labour's reputation for economic management."