Even those councils levying the maximum permitted increases would struggle to keep pace with social care costs and loss of government funding, the umbrella-body said.
Its survey of intended changes to council tax has found that all but five of the 152 top tier councils that handle adult social care will use the additional 3% precept allowed for this service, raising some £548m in all.
This, though, would be wiped out by the requirement to pay the national living wage and a potential £400m bill for back pay to sleep-in carers.
All councils can increase council tax by up to 2.99% without the need for the rare step of calling a local referendum to validate a higher amount - an increase of 1% from this year.
Most district councils can increase by £5 per year at B and D level.
Among top tier councils, 108 will increase council tax by 2.95% or more, the LGA found, raising £584m - far short of the £1.4bn the body claimed would be lost through cuts in central government funding.
It said 64 top tier councils would levy the full increase of 2.99% plus 3% for social care.
A further 75 would be unable to levy the social care precept in 2019-20 as they had ‘front loaded’ increases in this year and next and government rules permit only a 6% rise across the three years to 2019-20.
Only five top tier councils intend to freeze council tax completely this year.
The LGA said there would be a funding gap of £5bn by 2020, which would mean further reductions in services even where maximum council tax increases had been imposed.
LGA chair, Conservative peer Gary Porter, said: “The extra income this year will help offset some of the financial pressures they face but the reality is that many councils are now beyond the point where council tax income can be expected to plug the growing funding gaps they face.
“Extra social care funding will be wiped out by the significant cost pressures of paying for the government's National Living Wage and extra general council tax income will only replace a third of the central government funding they will lose this year.
“This means councils will have to continue to cutback services or stop some altogether to plug funding gaps.”
