Research by the County Councils Network (CCN) suggests three-quarters of English councils with social care duties are planning a 5% hike.
This is the maximum allowed without a local vote, and would add £100 a year to bills for average Band D properties.
The government said councils should consider money pressure on residents.
It said the amount local authorities will be able to spend next year was set to rise by £5.1bn, representing an average 9% rise for local authorities.
But council leaders say they have "little choice" but to raise tax in order to protect services, despite the rising cost of living for residents.
The CCN has analysed the budget plans of 114 out of the 152 councils in England with responsibility for social care that have published details so far.
It found 113 are planning to increase council tax, with 84 proposing a 5% rise from April and just one - Central Bedfordshire - keeping tax at its current rate.
The remaining 38 councils have yet to set out their plans. Three councils - Croydon, Thurrock and Slough - have special permission to increase tax above 5%, after effectively declaring bankruptcy.
Local authorities with social care duties will be able to raise council tax by up to 5% from April without consulting local residents, following an announcement at November's autumn statement.
One authority planning to increase by the full amount, Hampshire County Council, said even with the hike it would still need to dip into its reserves to fill a financial deficit next year.
The average council tax for a Band D property in England for 2022/23 was £1,966. A 5% rise would add £98 a year to bills for an average property from April, although the amount will vary across England depending on location.
Some council leaders say the council tax system is unfair, as it raises different amounts in different parts of the country. It is currently subject to a review by Levelling Up Minister Lee Rowley.