They have called on Boris Johnson to "act now" and set out proposals before Parliament's summer recess begins on 22 July.
There have been reports the PM would host a meeting this week with senior ministers to discuss reform ideas.
The government has pledged to publish funding plans by the end of the year.
In a letter to the prime minister, seven bodies representing those providing and using social care said the "time to deliver reform is now".
As well as long-term changes to funding, they also urged an "immediate" cash injection to cover short-term costs incurred during the Covid pandemic.
Councils in England should get money to invest in new technology, they said, and there should be a "new deal" for staff working in the sector.
The government has been criticised for not announcing new bill on social care funding at the start of the parliamentary year in May.
When he entered Downing Street in July 2019, Mr Johnson vowed to fix the funding crisis "with a clear plan we have prepared".
But reports suggest that discussions are still ongoing within government about the potential cost of changes, which could run into the billions.
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