The action by members of the Public and Commercial Services (PCS) union is scheduled for 15 March, the same day as chancellor Jeremy Hunt’s spring Budget.
It comes in addition to a four-day walkout by Border Force officials at four ports – Dover, Calais, Dunkirk and Coquelles – over 17-20 February.
At least 100,000 civil servants will take part in the action on 15 March, said the PCS, in an escalation in a dispute over pay, pensions and job security.
In a statement, the union said: "Our strategy calls sustained action in targeted areas where we can exert significant pressure on the employer, supplemented by all-member action called when its effect can be maximised."
