Almost a thousand council tenants could face eviction because they live in homes in Brighton and Hove with at least one spare bedroom.
Brighton and Hove City Council has indicated that it will take steps to minimise the risk of people being forced to move.
Under changes in housing benefit rules, tenants with spare rooms will have their benefit cut unless they and any dependents move to a smaller home.
An official report, which counted only adults of working age and excluded dependents, looked at measures to minimise the risk of a rise in evictions.
Ododo Dafe, a senior housing official, said that about £1 million was being provided by the government to the council to help people facing exceptional hardship.
She said that about half of the families affected by the changes wanted to move although there were few council houses or flats available for them to move into.
About half wanted to stay in the properties that they regarded as their home. Some face a loss of £1,180 a year in housing benefit with most expected to lose £606.
The council’s Housing Committee was told that the rule change did not affect pensioners, foster carers between placements, some parents of service personnel on active duty and some parents of disabled children.
A report to the committee explored the impact of the changes in the housing benefit social rented sector size criteria, known by its opponents as the bedroom tax.
It said that the council had “a strong track record of supporting initiatives that encourage social housing tenants under-occupying their current accommodation to downsize”.
It added: “The council is also committed to preventing homelessness and supporting tenants to maintain their current accommodation wherever possible.”
The report said that the housing benefit changes were part of a complex mix of welfare benefit reforms.
While the report looked at ways of providing help, it also said: “The council needs to be mindful of its fiduciary duties to council tax payers.”
Councillor Rob Jarrett said: “We have to be sympathetic to people who find themselves in very difficult circumstances.”
The Green councillor agreed with Labour spokesman Councillor Leigh Farrow about the need for a national co-ordinated campaign like the campaign against the poll tax.
Councillor Jarrett recalled appearing before Hove magistrates for refusing to pay the poll tax, or the community charge as it was formally known.
Conservative spokesman Councillor Mary Mears reminded the committee that the previous Labour government had brought in identical changes affecting tenants in the private sector.
She said that Green and Labour councillors had made no noise in that instance.
The committee agreed unanimously to adopt a set of measures to protect tenants facing hardship as the rule changes took effect.