A letter says the sector is on its knees following the Covid pandemic.
It calls for social care to have "its 1948 moment" to establish a "long-term and sustainable future" for the sector.
Boris Johnson has pledged to unveil the government's long-awaited social care plan later this year.
He has previously accepted that coronavirus has "highlighted the difficulties" in the sector.
Care England, a membership body for care providers, and the NHS Confederation, which represents health organisations, were among those to make the call in a letter to Mr Johnson.
Its 26 signatories wrote: "Successive governments have promised social care reform, but have not delivered and now the situation is desperate.
"Social care needs its 1948 moment to establish a long-term and sustainable future, that will be to the benefit of all citizens and the economy."
They noted that the sector was "on its knees" and "in desperate need of reform" after more than a year on the front line of the crisis.
They argued the current system leaves "many families struggling to survive" when one member needs social care, with thousands of people every year facing losing their home and family assets to fund care.
The letter's signatories have called for Mr Johnson to set out his reforms in the Queen's Speech, which is due to be held on 11 May.
Last month, Mr Johnson told the Commons Health and Social Care Committee it was "highly likely" that social care would get a mention at the event.
The letter was also signed by Age UK, social care provider UKHCA, and carers UK, as well as Liberal Democrat leader Sir Ed Davey and members of the House of Lords.
Lord Adebowale, chair of the NHS Confederation, has urged the government "to set out a clear timetable which details how reform of the sector can be delivered", saying this should be supported by "a long-term financial settlement".
"A well-funded and good quality social care sector is vital to a healthy nation and a strong and well-performing NHS," he added.
Meanwhile, Age UK's charity director Caroline Abrahams said: "Unless the government invests a lot more public money in care services now, the numbers of older people going without the help they need will simply spiral and more and more families will hit breaking point."
She has described the pandemic as "an object lesson in what happens if you starve care services of money and staff for year after year", saying "many thousands of older people died before their time".
"Nothing will bring those people back but the least we can do now is to restore services to a level of decency and give the staff on whom social care depends a proper career structure and the terms and conditions they deserve," she said.