Thousands of staff at the Home Office, including airport immigration workers, are to stage a 24-hour strike the day before the opening of the Olympics in a row over jobs, pay and other issues.
The Public and Commercial Services union (PCS) said its members will walk out on July 26, and will take other forms of industrial action, such as a ban on overtime, from July 27 to August 20.
The action will hit border controls at ports and airports including Heathrow, threatening disruption to people travelling to London for the Games.
The union warned it will announce further action if ministers continue to "refuse" to negotiate an agreement, warning that job and spending cuts are hitting services to the public.
The strike will involve staff across the Home Office, including the UK Border Agency, the Identity and Passport Service and Criminal Records Bureau.
PCS general secretary Mark Serwotka said: "The lives of staff have been made intolerable by these cuts and they're at breaking point.
"Ministers have known about these issues for a very long time and need to act now to sort out the chaos they have caused.
"They're acting recklessly in cutting so many jobs and privatising services, and are provocatively refusing to talk to us with a genuine desire to reach an agreement."
Home Secretary Theresa May branded the PCS strike decision "shameful".
"I think that is shameful, frankly," she said in a round of broadcast interviews.
"They are holding a strike on what is one of the key days for people coming in for the Olympic Games.
"We will of course put contingency arrangements in place to ensure we can deal with people coming through the border as smoothly as possible."
Earlier, Labour leader Ed Miliband spoke out against disrupting the Olympics, saying: "People should not be striking during the Olympics. People should not be disrupting the Olympic Games."
Prime Minister David Cameron condemned the strike, insisting the Olympics would be safe and secure regardless of any industrial action.
Speaking at a press conference in Kabul, the capital of Afghanistan, he said: "I do not believe it will be right, I do not believe it will be justified."
Union officials said a work-to-rule and overtime ban could have a big impact on border controls and in passport offices because of the amount of overtime worked.
The PCS is in dispute with the Home Office on several issues, including plans to cut 8,500 jobs, the threat of compulsory redundancies in the passport office in Newport, South Wales, pay rises capped at 1% following a two-year wage freeze, privatisation of services, and alleged victimisation of union reps.
Mr Serwotka said the issues which have caused the dispute were flaring in other Government departments, which could also lead to industrial action.
The union said cuts in the Border Agency was causing "chaos" and leading to long queues at airports such as Heathrow.
PCS members at the Department for Transport, including driving test examiners and Coastguards, have been taking industrial action over the past few weeks, while staff in other Government departments including the Ministries of Defence and Justice, are set to vote in the coming weeks on how to campaign against cuts.
Around 16,000 PCS members in the Home Office took part in a ballot, with a 57% vote for strikes and 75% majority for other forms of action, on a turnout of 20%.
Baroness Jo Valentine, chief executive of business group London First said: "Calling a strike on the demand of 12% of members is ridiculous. This action shows a cynical contempt for the public by a minority of PCS members.
"At a time when everyone wants the UK to look good and show the world what it is capable of, the PCS is behaving like a sulky child who isn't getting his own way."
John Cridland, director general of the CBI, said: "As the world arrives in London for the Olympic Games, every one of us should be giving our guests the warmest possible welcome. For PCS to go on strike on this key day beggars belief. For it to happen because of a vote by 11% of staff is simply outrageous."
Labour MP John McDonnell, who chairs the PCS Parliamentary Group, said: "The Government has brought this dispute on its own head. The UKBA and passport staff have been raising their concerns over job cuts and the impact on services for over 12 months now.
"The PCS Parliamentary Group only met the minister three weeks ago to warn him of the low morale caused by the Government's actions and the urgent need to stop compulsory redundancies."