1,300 employees of the Atomic Weapons Establishment (AWE) in Berkshire were to be balloted on Tuesday over a "derisory" 2 per cent pay rise offer.
Workers have threatened to go on strike over poor wages and unsafe working conditions.
According to an officer of the trade union Prospect, votes will be cast by 16 November.
Strikes are possible by the end of this month.
AWE which is under the management of an industrial consortium comprising outsourcing company Serco, US weapons maker Lockheed Martin and engineering group Jacobs has said in a statement that the decision of the union was "extremely disappointing."
The company added that it had made the "best offer possible in the current economic climate," saying it had to cut costs to comply with Treasury cuts.
"We are not asking for inflation-busting pay increases but just something that reflects the hard work that people do," said a spokesperson for the workers.