Thousands of families in the city will be affected, leading to fears many will fall into arrears because bills are expected to rise by as much £100 a month in some cases.
The changes, part of the Government's welfare reform agenda to reduce the benefits budget by £28billion, begin in April with the under-occupancy rule, or 'Bedroom Tax', as it has been labelled.
Tenants who claim housing benefit and rent from a registered social landlord (housing association or local council) will have their benefit cut if the new rules decide they have a 'spare' bedroom.
For one spare bedroom housing benefit will be reduced by 14%. For two or more spare bedrooms a 25% cut will be applied.
The cut will hit single people and couples who have not yet reached pension age, but are still living in the house where they raised their children or one of a similar size and now have spare bedrooms.
It will hit families who have children up to the age of 16 of the same sex with a bedroom each or two children under 10 of either sex with a room each.
People of State pension age are not affected by the changes because they are no longer of working age.