Harrow's Labour group says more than 550 people have been affected by Government changes to benefits.
The Government reforms that cut housing benefit for council tenants with spare rooms are referred to as the ‘bedroom tax’ by opponents and the 'spare room subsidy' by supporters.
According to Harrow Borough Council's Labour group, 577 people have been affected by the changes, but only 35 of them have been able to move to a smaller property due to a shortage of council properties.
The group says this means only six per cent of people affected by the reforms have been able to avoid paying more for their council property.
Labour group leader Councillor David Perry said: “The cruel and unfair bedroom tax has hit the poorest in Harrow hard. I am proud that the Labour Party has promised to abolish it.
“In Harrow the Labour Group wants to tackle the root causes of the bedroom tax.
“One of our key pledges is to build more affordable homes by restarting a council house-building program.
“Instead of penalising people, Labour will ensure residents of Harrow have somewhere decent and affordable to live.”
The Conservative group's housing spokesman Cllr Barry Macleod-Cullinane said: "It's important to stress that the cap is affecting fewer households in Harrow than predicted, and not all those affected necessarily want to move.
“However I genuinely understand the difficulties faced by those who want to but can't because of a lack of smaller properties.
“This is why our Conservative administration is surging ahead with plans to build 700 new council properties.
“What I find incredible, however, is being lectured on the need for more housing in Harrow by Labour.
“They didn't build a single council house during their three years in power, and now because there's an election on the horizon they're suddenly pretending to care about tenants.
“Housing in Harrow is a complex issue, and we're taking bold action to tackle the challenges it presents.”