The County Councils Network (CCN) says a 1% increase would raise just £105m compared to the £1bn cut being imposed on rural authorities by 2020.
They warn they will be forced to cut bus services, children’s centres and libraries and impose new charges for social care, and there will be less money for road maintenance and pothole repairs.
According to the CCN, most counties will be increasing council tax by the extra 1% to help make up the budget shortfall.
The CCN says county council leaders are lobbying their local MPs in the lead up to the parliamentary vote on the final local government settlement, arguing for an extension of the £300m transitional funding package introduced last year.
They say core funding will be reduced by almost half by 2020 and if they are not given extra money they will have to raise council tax next year which would reinforce the inequality they face compared to towns and cities.
CCN chairman Paul Carter said: 'Over the past seven years shire counties have faced the toughest financial challenge of all, with rising demand for services meaning we already face a £2.54bn funding black hole in 2020/21.
'This comes on top of being the lowest funded councils.
'The ending of essential grants this year for frontline and life-critical services means we are facing some truly unpalatable budget decisions, which will see rural bus subsidises all but end, new charges for care services, children’s centres and libraries disappear and potholes go unfilled.'
Heather Jameson reveals analyses the impact of a 1% council tax increase.