Thirty five families have moved house since April as a result of the bedroom tax, according to a report in the Brighton and Hove Independent.
The free weekly newspaper said that the figure for the past year was 200 households swapping their council house or flat.
It quoted Brighton and Hove City Council saying that hundreds of tenants were struggling financially after benefit reductions penalised people deemed to have spare bedrooms.
The council said that many growing families needed bigger homes which was why it was encouraging swaps.
Councillor Bill Randall, chairman of the council’s Housing Committee, said: “Brighton and Hove is already facing a rising tide of homelessness and a growing demand for affordable housing.
“Now hundreds of council households are dealing with the added dilemma of whether to pay more every week for a spare room, find a lodger or move.
“The council is doing everything it can to help these households in most cases families are really happy with their move.”