Unison and Unite, the sector’s largest and third-largest unions respectively, are balloting members over strike action on the deal, worth 2.45% to most members and 3.3% to the lowest paid.
GMB members voted four to one to accept Local Government Employers’ offer.
Brian Strutton, GMB national secretary, said the decision was not a vote of satisfaction with the deal.
This pay offer is only being accepted because the alternative would be strike action and many members cannot afford to lose pay to go on strike,” he said.
“That is the economic reality, but it is clear from feedback that the mood is changing.”
Heather Wakefield, Unison’s head of local government, said the GMB decision was “unfortunate” but not surprising after the union advised its members that the tabled deal was the best that could be obtained without strike action.
She said it did not undermine the potential effectiveness of any future strike: “Unison and Unite constitute the majority of local government union members, so we’ll do whatever our members want us to do.”