Council tax bills in England are set to rise by an average of 3.5% this April, according to a survey by the Local Government Association.
Some councils are struggling to fund services, the LGA says
The figures are based on draft budgets from just over a quarter of councils, which have until March to finalise their plans.
If the trend in the survey continues it would be the second lowest rise since the council tax was introduced.
It would add just under £44 to the average band D bill of £1,268.
Individual figures in the survey of 127 local authorities do vary, with some councils reducing their charge.
Conservative-run Hammersmith and Fulham, for example, plans to reduce its charge by 3%.
But many county councils are putting up their charges by 4.9%, just below the point where they would be capped by the government.
One council, Conservative-run Tewkesbury was planning a rise above the limit.
The Local Government Association (LGA) warned many of these councils were struggling to meet increasing costs, particularly in care for the elderly.
LGA chair Lord Bruce-Lockhart said unless the government gave authorities more money care for older people would suffer.
"Without additional funding, local government may potentially face a situation, by as early as 2009, where it cannot afford to provide support to the 370,000 people with lower levels of need," he said.
Lord Bruce-Lockhart also said some of the rises had been caused by a higher than expected demand for free bus passes for the over-60s.
He told the Times newspaper: "The free bus pass was a good idea but it hasn't been funded so it has become another pressure on the council tax bill which the elderly cannot afford to pay."
Local government minister Phil Woolas said he was certain the low average rises so far were the result of government investment in local authorities.
He said: "It is encouraging to note that, as reported by the LGA, local authorities are driving down council tax rises without sacrificing improvements to public services."
He added that the government would not hesitate to use powers to cap any authorities which propose "excessive" increases.
Campaign group Is It Fair, which wants the tax replaced by one more linked to ability to pay, said any rise would be hard for many pensioners and others on fixed or low incomes.