The carer’s allowance benefit should be overhauled and the basic rate of payment increased to lift more unpaid carers and disabled people out of financial hardship, according to a living standards thinktank.

The Resolution Foundation said unpaid carers on low incomes were paying a “very heavy price” – a typical penalty of 10% or as much as £7,000 a year compared with non-carers – for looking after loved ones full-time.

It called for the basic rate of carer’s allowance – currently the lowest-value benefit at £83.30 a week – to be raised to at least the £92.05-a-week rate of jobseeker’s allowance to help improve miserable living standards for the poorest carers.

It also called for the removal of the notorious “cliff-edge” penalty on carer’s allowance claimants’ earnings, currently capped at £196 a week, to enable more unpaid carers to supplement incomes with part-time work.

The harshness of the cliff-edge earnings penalty, coupled with failures in the handling of carer benefits by the Department for Work and Pensions (DWP), caused hundreds of thousands of carers to unwittingly run up huge overpayment debts in recent years.

Resolution’s report comes as the disability policy expert Liz Sayce prepares to hand ministers her independent review of the carer’s allowance – commissioned in response to an award-winning Guardian investigation into the treatment of vulnerable unpaid carers by the DWP.

Hannah Slaughter, the Resolution Foundation’s senior economist, said ministers need to review support across the board for unpaid carers: “The trend of rising levels of disability across Britain, and the need for unpaid care, isn’t going to end. It’s time policy caught up with this reality,” she said.

About two-thirds of unpaid carers experienced material deprivation – defined as the inability to afford essential items such as food and energy – while carer social security benefits were often inadequate to protect family incomes, Resolution said.

Despite UK family members effectively providing £184bn a year of unpaid care to loved ones, the value of carer’s allowance has fallen in the last two decades from 32% of full-time earnings at the minimum wage to just 19%, it found.

Bringing the relative value of carer’s allowance back up to 1999 levels of 32% would boost the benefit by £53.45 a week to £136.75, at a cost of £2.9bn a year, the Resolution report said. An alternative would be to raise carer’s allowance rates in England and Wales to £94.60 a week, in line with the enhanced rates in place in Scotland.

Slaughter said: “There are now over a million working-age families in Britain that include both a disabled person and an unpaid carer – and they are paying a heavy financial price for these circumstances.

“More must be done to boost the living standards of disabled people and their carers. Employers should improve their retention of disabled staff and carers, and the government should raise the value of unpaid care in the benefits system and extend carers’ leave.”

Emily Holzhausen, the director of policy and public affairs at Carers UK, said: “The evidence from the Resolution Foundation’s report adds even more impetus for change to improve carers’ benefits, especially after the scandal of overpayments of carer’s allowance and potential cuts to welfare benefits.”

A government spokesperson said: “We understand the huge difference carers make, as well as the struggles so many face.

“That’s why we have raised the carer’s allowance earnings threshold by £45 a week to £196, benefiting more than 60,000 carers by 2029-30. This is the biggest ever cash increase in the earnings threshold for carer’s allowance.

“We have also launched an independent review into social care, part of which will explore the needs of unpaid carers who provide vital care and support.”