South Hams District Council in Devon has petitioned the government to end the current 10% council tax rebate on second homes.
The council's LibDem leader wanted to increase the tax 200% on second homes in the district but this was not passed.
Any council tax increase would apply to the 4,172 local second homes in the district.
There are 250,000 second homes in the UK dominated by the south west.
Nearly half the homes in Trebetherick in Cornwall are second homes.