Residents are being warned bin collections could be hit by a third strike as workers walk out at Hull's main recycling site.
The trade union Unison said members were "in it for the long haul" and industrial action may become "indefinite".
The action will see pickets at the Wilmington waste recycling site from tomorrow until May 14, which could lead to delays of several days in bin collections and queues at household recycling sites.
It follows fruitless talks with management at site owner FCC Environment, who are refusing to extend the company sick pay scheme that they enjoy to workers on the frontline.
One worker who got cancer had to return to work because there was no sick pay.
Unison regional officer Joe Gibbins said: "The vast majority are very low paid, on the minimum wage, and if they get ill, they get statutory pay which is peanuts, despite the fact they are working with hazardous materials.
"All they want is to be treated with parity. In this day and age it is Dickensian.
"We are reasonable people but when organisations are turning a profit that's some small developing country would love, it is not acceptable.
"It will cause further disruption, there will be a backlog of bins. It will add extra time for the guys in the East Riding and Hull to empty.
"People could be collected two or three days late and there will be queues at recycling sites."
Mr Gibbins said there was talk of the next strike - which would be the fourth - lasting a month, and it could even become indefinite.
He said: "The members will make that decision. The men are absolutely solid. They are in for the long haul. The last vote for industrial action was unanimous - and even the guys who do get sick pay are 100 per cent behind it - these guys aren't giving up."
Hull Council has warned residents of "potential disruption" on its website.
They said: "Due to industrial action between our waste contractor FCC and Unison, there may be disruption to waste collection services in Hull between Tuesday 1st May and Monday 14th May.
"Due to the disruption, collections may be earlier or later than normal so we would encourage residents to make sure their bin is presented for collection by 7am.
"We appreciate residents’ patience through this period of potential service disruption.
West Hull and Hessle MP Emma Hardy raised the issue in Parliament earlier this month.
Speaking at the time she said: "It’s not good enough for a firm that is receiving public money in the form of government contracts to not pay sick pay because it would rather put that money towards profits for shareholders.
"I’m fully on the side of the workers in this dispute and have been down to the picket line twice already, they are doing everything they possibly can to come to a consensus with FCC and have even suggested they will give up their annual bonuses to secure this sick pay.
"It’s time for FCC to be reasonable and pay up and I’ll be doing everything I possibly can to make sure this happens.”
East Riding Council said it didn't expect any of its sites managed by FCC Environment to be affected.
A spokesman said: "We have been assured by FCC Environment that all of those sites will be open and running as normal during the proposed strike action.
"Residents will still be able to visit our household waste recycling sites, which are open from 10am to 5pm seven days a week.
"This action is not expected to affect bin collections and we ask residents to continue putting their bins out as normal."
FCC declined to comment.