The action could include up to 3,000 workers at Stanlow, Fawley, Valero, Grangemouth and Mossmorran oil refineries, as well as at Sellafield Nuclear Facility.
Strike votes are also expected at Drax and Hartlepool nuclear power station in the coming days.
The workers, who are covered by the National Agreement for the Engineering Construction Industry (NAECI), voted to turn down a pay rise of 8.5% for 2024 and 3.5% for 2025.
More than 50 GMB and Unite reps from across the industry will now meet to discuss next steps.
GMB national officer Charlotte Brumpton-Childs said: “Our members’ pay has fallen over 20% behind inflation. The employers have forced our members into a position where they are taking part in industrial action ballots of this scale for the first time in their careers. The message from the workforce is loud and clear: value their work.”