They also noted employers were increasingly suffering the departure of staff who have been forced to care for family members in the absence of sufficient state support.
Their calls were tempered by John Redwood MP, chair of the Conservative economic affairs committee, who claimed the reforms identified by the Dilnot Report focused too heavily on "trying to protect the inheritance of children of the elderly".
He suggested instead that more emphasis should be put on those who could afford it contributing more for their care, including from their estate.
The open-letter published by the Daily Telegraph was signed by 72 cross industry representatives, including Otto Thoresen, director general of the ABI; Mark Ellerby, managing director of Bupa Care Services; Baroness Greengross, chief executive of the International Longevity Centre; and James Lloyd, director of the Strategic Society Centre.
It said the current system was failing to meet the challenge of supporting the increasing number of people who need care, "resulting in terrible examples of abuse and neglect in parts of the care system".
"This comes at huge cost to the dignity and independence of older and disabled people, but also to our society, family life and the economy.
"Businesses are losing increasing numbers of experienced staff who are forced to give up work to care for older or disabled relatives.
"These carers can then be pushed to breaking point, providing round-the-clock care.
"Our NHS is also paying the price, as a lack of support leads to avoidable hospital admissions and then keeps older and disabled in hospital beds because they cannot be cared for at home," it added.
The letter concluded by saying the situation required strong political leadership.
"We urge the government and the other party leaders to seize this opportunity for urgent, fundamental and lasting reform: delivering a social care system which can provide the well-funded and high-quality care and support we would all expect for ourselves and our families."
Speaking on BBC Radio 4's Today programme, Richard Humphries, senior fellow in social care at the King's Fund, said the current situation was not acceptable or sustainable.
"Everyone accepts we can't go on like this," he said.
"We're going to see more and more people go without the care they need and will see more pressure on the vast army of unpaid carers and on the NHS.
"The NHS will not work properly unless we sort out social care funding," he added.
However, Redwood responded by demanding those who could afford to pay more, should do.
"If somebody is very rich, why shouldn't their estate make a contribution to that?
"Payment could be deferred to allow the elderly person to get best possible care and attention and then the bill settled out of their estate after they unfortunately died," he added.
Lord Warner, who was part of the Dilnot Committee, noted that increasing a £50,000 cap on care fees was a possibility but that "we will not push up the quality of care without increasing the size of the social care pot.
"That needs to be increased by contributions from taxpayers and individuals and families."
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