The RMT had balloted its 800-strong membership of divers and support workers, who are seeking a 50% wage rise, on the employers' latest offer.
The union claimed divers earnings had slipped by nearly 20% since 1984, when compared with average UK earnings.
The offer was decisively rejected by 640 votes to two, with the union giving notice that only a dramatically improved offer could now avert strike action from starting on 1 November.
RMT
