The union said members across the BBC, including the World Service, are at risk of compulsory redundancy.
The BBC said in a statement that it was disappointed by the union's actions. It said it had no choice but to meet savings targets that will require job cuts.
The BBC is funded mainly by a mandatory 145.50 pounds ($228) annual levy on all households with color TVs. Britain's government froze the fee in 2010, and the corporation has been forced to make cuts.