More than 60 staff staged an unofficial strike after a colleague was suspended last week in a row over boundary changes.
Those involved in yesterday's rally work mainly with vulnerable people, including the homeless, refugees and those in prison.
One member of the homeless casework team said: "The workload has become far too high for us to deal with and repeated requests to increase staff have not been followed up with anything.
"Stress levels are through the roof, morale is very low and we don't see any way out from what we're being offered.
"We're telling single males on a daily basis that we don't have anything for them, and to come back the next day."
Employees blame budget cuts and restructuring for the increase in workloads.
Some cited the use of private hotel rooms for the homeless as one area where money could be put to better use employing staff.
A council spokesman said: "This unlawful industrial action is completely unacceptable and those involved are liable to be dismissed if it continues.
"We are fully aware of the pressures on the homelessness service and have been taking steps to address staff concerns.
"We were scheduled to meet Unison to resolve those concerns on Wednesday, but there is no prospect of that happening against the backdrop of an illegal strike."