Council leaders have said the government's plan to provide free home care would cause cuts to existing services.
In a letter to TheTimes, councillors said the Personal Care at Home Bill would heap further strain on an already overburdened social services system.
They said the Bill – going through Parliament – had "major weaknesses" and problems with funding.
Under the plan, 400,000 vulnerable elderly people would receive personal care at home. However, it would cost £670m per year. Of the £670m total, £420m is to come from existing Department of Health budgets, with local authorities expected to provide the remaining £250m from efficiency savings.
Critics of the plan have questioned its funding, saying the government had underestimated how many people would use the service and what its full cost would be.
The 78 signatories, representing all three major parties and every region in England, wrote: "We fully support the principle of providing additional support to those with the most critical care needs.
"What we cannot support, however, is a piece of legislation that has major weaknesses and which risks adding further strain to an existing system already under considerable financial pressure."