Under new UK Government welfare rules, working age tenants will have their payments reduced by 14% for having one unoccupied bedroom and 25% for having two or more.
In a report to the council's Corporate Management Team, executive director of Housing and Social Work, Mary Castles, revealed the likely impact of welfare reform.
Of the 295 claimants questioned, 156 will have to cut their spending in other areas just to meet rent payments and 55 will have to move to a smaller home.
Fewer than 20% of tenants are 'very confident' of being able to make up the difference when their housing benefit is cut from April 1.
At-risk households were identified from housing and social work records and visited by welfare rights officers and social workers.
Mrs Castles said: "We have already taken on additional staff to advise tenants and wrote to around 6000 we believe will be affected by the Bedroom Tax.
"These changes present an unprecedented challenge for the council."
Council leader Jim McCabe described the Bedroom Tax as "the single worst piece of legislation" he has ever seen.
He added: "It threatens families, threatens lives and threatens the fabric of our society.
"We have offered personal visits to talk people through the changes."