Ministers insist local authorities can keep council tax rates low despite extra demands on social care funding.
The Government said adequate provision had been made to meet care needs as it was reported some authorities could hold local referendums on whether to breach a 5% cap on council tax increases.
Surrey is considering asking voters to back a 16% rise, according to the Daily Mail.
But the Department for Communities and Local Government (LCLG) said council tax bills should be kept low.
A spokesman said: "Our long-term funding settlement means local authorities will have nearly £200 billion to spend over the course of this parliament. This should allow them to deliver high-quality services that local people want while keeping council tax bills down.
"We've also just announced an extra £900 million for social care, meaning they will have a total of £7.6 billion to spend over four years."