Council workers in Southampton and Doncaster were also set to join the walkouts on 30 June.
Some 5,000 council workers across Doncaster were to strike for the day.
It comes after they voted by 66 percent for strikes.
The workers are fighting 700 job cuts.
The union moved fast to ballot over the threat of cuts before the details were announced.
“We balloted on principled trade union grounds: against the threats,” said Doncaster Unison branch secretary Jim Board.
“They only put out a story in the middle of the ballot period confirming the job cuts.
“And that just ramped up the temperature.”
The workers were set to join a joint South Yorkshire strike rally in Sheffield.
In Southampton, more than 200 Unison and Unite union members were to strike for a week, and join a demonstration with other striking workers on 30 June.
And the unions also plan to escalate the action again next week by bringing out a section of social care workers for a week, to join the six parts of the council who have already struck.
The workers are fighting the council’s plan to sack them all this month if they do not take 5 percent pay cuts.
The cut will mean that many workers will stand to lose up to £1,000 a year.
The unions have called a joint members’ meeting on Monday of next week to discuss the way forward for the action—just a week before the sacking notices take effect.
The workers will need to argue for a dramatic escalation of the strikes to win.
Support for their fight is growing.
Speech after speech at Unison’s annual conference last week pledged solidarity with the strikes.
The union’s general secretary Dave Prentis was set to join the march and rally starting in the city’s Each Park on 30 June.
The action is spreading across the union. The latest people to join the action are housing repairs workers in the London borough of Camden.
They voted by 83 percent for strikes.
Striking workers from across Camden were set to join their picket lies on Jamestown Road on the morning of 30 June.