Dorset County Council will increase its share of the council tax by just under 2% next year.
It already need to cut £15 million this year and the council says it would have to save even more if they didn't increase their share of the council tax.
Council tax in Swindon is set to remain frozen for the fifth year in a row.
The recommendation to keep it at its current level will go before cabinet members next week, when they are due to decide on next year's budget.
Somerset County Council today announced that people whose homes are flooded or cut off because of the floods will not have to pay the County Council part of their council tax until they are back in their homes.
Leader of the Council, Cllr John Osman, said: “We recognise that local people affected by the flooding are struggling and under tremendous strain.
“We want to remove one of their financial worries by suspending their council tax charge while they are stranded or unable to live in their home.
“There are some people who are being asked to pay council tax both on their home that they have had to leave under traumatic circumstances, and also where they are now in emergency accommodation. That can’t be right and we are reacting quickly to reassure people.
“We are in talks with our District Council colleagues to see if they are able to follow our lead and also suspend their part of council tax for flood victims.”
Council tax in North Somerset will rise by 1.5% in the year ahead.
The decision was made at last night's [Tuesday] full council meeting. The rise equates to a 33p a week rise for an average Band D property, with an annual bill of £1,164.88 - a rise of £16.95.
Councillor Ashton added that government grant funding had been reduced by 6.3% for 2013/14 but that the council is still waiting for confirmation of the final settlement. He added that it is because of unfair funding that the decision to raise council tax has had to be taken.
Full details of the council tax amounts by council tax band and parish can be found here.