Both Labour and Conservative councils have complained falling Government funding and rising demand as people live longer have left them facing a care crisis.
The letter continues: “Given the scale of rising demand, this immense challenge will face whichever Party is in government over the coming decades.”
She said: “We need to do our best for our elderly and vulnerable residents in the face of such severe Government funding cuts.
Councils could already raise bills by two per cent plus a further two per cent through the so-called social care precept.
Theresa May will come under further pressure to confront the crisis with the publication of a joint letter from three senior MPs calling for a cross-party agreement on the future of health and social care funding.
Local Government Secretary Sajid Javid announced before Christmas councils will be allowed to raise the social care precept by three per cent this year and next.
But Yorkshire councils are complaining the Government’s approach will put them at a disadvantage as a one per cent rise in many parts of the region will raise far less than more affluent areas of the country.