UNISON members have now backed walking out as a row over compensation payments continues.
It follows an announcement on Tuesday from the GMB that its workers had voted to support strikes.
Unite the union is also asking its members whether they want to take industrial action, with a ballot running until March 14.
What is the dispute about?
A £500 million settlement was agreed with thousands of council staff in 2019 but a new pay and grading system needs to be introduced as many, predominantly female, workers continue to be paid unfairly.
Pay claims up to March 31, 2018, were settled by the 2019 deal, however there are new claims for the pre-2018 period as well as demands for further interim payments for after 2018.
The unions have said there has been progress on the new claims for pre-2018 but around 18,000 claimants are waiting on a settlement for the post-2018 period.
A council spokesman said the new pay and grading structure was delayed by the pandemic, with agreement from the unions, and that they also agreed new claims should be settled before talks on the period after 2018.
What is UNISON saying?
Lyn Marie O’Hara, UNISON branch depute chair, said: “This is a huge vote for action and a clear message to the council to resolve the dispute.
“The UNISON branch will now request authorisation for strike action from our NEC and be liaising with our sister trade unions on the next steps in the industrial dispute.
“The trade unions will also continue to receive regular updates from the claimants joint legal team on the current negotiations with the council lawyers. The council should now listen.”
Just under 9,000 workers were balloted by UNISON, with a turnout of 52.5 per cent, and 96 per cent of voters backed strike action.
It covered workers in home care, cleaning, catering, nurseries, schools, care homes, homelessness hostels and admin and clerical teams.
What is the council saying?
The council spokesman said: “We’ll await the details from the union. However, it remains disappointing that they balloted members when we have been clear we are ready to make offers on new claims.
“It was agreed with unions that new claims should be settled before we discuss the period after 2018.
“Delays to the implementation of a new pay and grading structure, caused by the pandemic, were also agreed — unions specifically didn’t want members taking part in evaluation interviews during that period.”