About 20 Hull waste recycling workers have begun a two-week strike in a row over sick pay.
Unison members have walked out from the Wilmington and Driffield sites again after first taking action on 1 March.
They said staff faced "hazardous and contaminated conditions" and were not being looked after by employer FCC Environment.
FCC said it had tried to "resolve the situation". The city council said it was trying to "minimise" disruption.
Unison officers said it had "fruitless talks" with FCC bosses but the firm was "steadfastly refusing to extend the company sick pay scheme" to frontline workers, which "reflects very poorly" on the business.
Joe Gibbins, Unison's regional officer, said: "It seems remarkable that in this day and age workers who face hazardous and contaminated conditions are not even looked after by their employer when they fall sick."
He said the union was helping employees "fight for better conditions and support" and called for the local authority to "review whether it is morally right to allow them to continue in this way".
He added: "I hope they see the error of their ways and are able to resolve this issue."
An FCC spokeswoman said: "We have had a further meeting with the union to try to resolve the situation. Our offer is a fair offer and it still stands."
In a statement, Hull City Council said: "We are supporting both parties to reach the quickest possible resolution and doing everything we can to maintain our services for residents."
A council spokeswoman said bin collections would "remain operational", but that collection times were affected by the strike and householders should leave their bins "out for longer".