Border Force staff are among more than 130,000 civil service workers who have voted to strike at the end of April.
Workers are set to walk out on Friday 28 April, in the latest round of industrial action.
The PCS union, which represents hundreds of thousands of government workers, as well as those at the Maritime and Coastguard Agency, has been calling for a pay rise, better pensions, job security and no cuts to redundancy terms.
Members from 186 different employers were balloted over the latest strike action last week, the PCS union said.
“Our members are not backing down in this dispute,” said PCS general secretary Mark Serwotka.
“Ministers need to take notice that we’re escalating our action and they need to resolve the dispute by putting money on the table.
“We know our strikes have already caused serious disruption. The new strikes and another national day of action will pile the pressure on a government that refuses to listen.”
The Home Office advises passengers due to travel around this date to check the latest advice from their travel operator.
It adds that those travelling to and from the UK should prepare for “longer wait times”.
“Our first priority is to keep our borders safe and secure. We will never compromise on this,” it said in a statement.
“Please be patient and respect officers who are working to keep our citizens safe and border secure, and supporting travellers during the strike action.”
The news follows the announcement that Passport Officer workers will strike for five weeks this spring in an escalation of a dispute over jobs, pay and conditions.
More than 1,000 members of the PCS union working in Durham, Glasgow, Liverpool, London, Newport, Peterborough and Southport will walk out from 3 April to 5 May, while those in Belfast will strike from 7 April to 5 May.
Downing Street said ministers would work to “mitigate” the impact of strikes by Passport Office staff.
“The Home Office will work hard to manage the impact of this strike action to ensure they can still provide the vital service to the British public as you would expect ahead of the summer where we fully acknowledge that many people will want to get away and enjoy the summer with their family,” a spokesperson said.
