The 7,000 members of the county federation voted for the resolution at its annual meeting last week.
They are now hoping it will be selected for a national WI debate, which would take place in 2009.
Jean Johnson, Hampshire WI advisor, said that if the resolution was successful nationally the WI would put it forward to the government.
She told BBC News: "We really felt the local authorities should license premises so that they were safe working space providers.
"It could be your daughter, your granddaughter or even your son"
"Prostitution cuts across the classes but it's often the girls from the lower classes who have it worse."
She said by legalising brothels, the health of working girls and their access to medical care could be improved, while it would also make it easier for police to tackle illegal human trafficking.
"There were a lot of people who were surprised when we first started talking about this," Mrs Johnson said .
"Initially people were saying 'you should leave that subject well alone'.
"But we said it could be your daughter, your granddaughter or even your son."
She said the debate begun as a result of the high profile investigation into the murders of five women in Ipswich last year.
Gemma Adams, 25, Tania Nicol, 19, Anneli Alderton, 24, Paula Clennell, 24, and Annette Nicholls, 29, who all worked as prostitutes, were found dead in December 2006.
Steve Wright, 49, of London Road, Ipswich, is due to stand trial in January accused of murdering them.
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