Hiking up council tax bills to cover the social care funding black hole will increase the postcode lottery in provision, Theresa May was warned amid speculation she will back steep rises in the levy.
Experts have issued fresh warnings that the straining system could "topple over at any moment" leaving the poorest "living a squalid life".
The Prime Minister is reportedly preparing to allow tax precepts to be increased so local councils, which have suffered reductions in government grants totalling more than 40% since 2010, can claw in extra cash to cover the spiralling social care costs.
Martin Green, chief executive of Care England, which represents care home providers, told The Times: "The whole thing could topple over at any moment and those who are poor and vulnerable will suffer most."
Andrea Sutcliffe, the chief inspector for adult social care, told the newspaper: "The system is approaching a tipping point. We've got increased demand and potentially a restriction on capacity.
"Unless we really get to grips with some of these problems... we will get to an absolute crisis."
Labour's Lord Lipsey, who was involved in a Royal Commission on elderly care funding in the 1990s, added: "There could be mass closures of care homes.
"There's a danger that poor people in poor areas will end up without care, living a squalid life. There could be care black spots because the homes that are reliant on state funding will become unsustainable."
Former chancellor George Osborne introduced a 2% precept to pay for care for the elderly and disabled.
Town halls have warned that even if every council imposed the maximum extra levy, social care would still face a funding gap of at least £2.6 billion by 2020.
Liberal Democrat Shadow Secretary of State for Health Norman Lamb said: "This is dreadful crisis management from the Conservatives.
"They are lurching from crisis to crisis and this is yet another desperate sticking plaster solution which falls short of what is needed.
"Making councils bear all the burden will increase the postcode lottery which already exists.
"It will mean that wealthy parts of the country will find it easier to meet rising demand whilst those areas where council tax raises less money will be left struggling.
"The Government must be held to account for the consequences of leaving more and more people without the care they desperately need."