It’s a grand day to be Irish. At least, that’s what many Britons appear to think. The Irish government isn’t so sure.

Irish post offices have run out of passport application forms and are getting 4,000 passport inquiries per day versus the typical 200 per day in the wake of the U.K. vote to leave the European Union, according to Reuters. “There has been a spike in interest in Irish passports,” Irish Foreign Minister Charlie Flanagan said in a statement. “The increased interest clearly points to a sense of concern among some U.K. passport holders that the rights they enjoy as EU citizens are about to abruptly end. I want to state clearly that this is not the case.”

There were signs of a surge in passport applications hours after the U.K. referendum result was known. Last Friday, Google U.K. GOOG, -2.37% searches for “getting an Irish passport” spiked 100% in the immediate aftermath of the U.K. vote to leave the European Union, the first such country to do so since the formation of the political and economic union three decades ago. Ireland’s Department of Foreign Affairs even published a guide to getting an Irish passport in the wake of the vote. “Ireland is a strong, open and competitive economy,” Irish Prime Minister Enda Kenny said Friday.

Holders of an Irish passport would have the freedom to work anywhere within the 28-member union and have the right to “visa-free or visa-on-arrival” travel to 172 countries around the world, according to global advisory firm Henley & Partner’s Visa Restrictions Index, which places the access given to holders of Irish passports in a tie for No. 6 in the world. Despite austerity measures imposed on it by the EU in recent years, the country remains solidly pro-Europe.

Another advantage to having an Irish passport: Irish citizens are only liable for Irish income tax if they are resident there — as opposed to the U.S. citizen who is responsible for U.S. income tax regardless of their residence, according to Offshore Investment, a magazine aimed at ultra-high-net-worth individuals around the world. “Irish citizens can enter the U.S. and remain for up to 90 days without a visa and have similar privileges in 83 other countries world-wide.”

The Irish government said there has been an increase in inquiries about acquiring Irish passports but noted that the withdrawal of the U.K. from the EU will take at least two years. During this time the U.K. will remain a member state with no changes to current freedoms for EU citizens to travel and work between Ireland and the U.K., Ireland’s Department of Foreign Affairs said in a statement. “Every effort will be made to minimize any changes to these arrangements.”

Still, judging by the inquiries about and searches for Irish passports, many people in the U.K. who want to be free to travel and work within the 28-member EU don’t want to take any chances. There are around 430,000 Irish-born people residing in Britain, according to the 2011 Census, but the Department of Foreign Affairs said estimates vary as to how many are second-generation and beyond Irish people. “However, one in four people in Britain have Irish heritage.”

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It’s easier for some Britons than others to get an Irish passport. If you were born outside Ireland to an Irish citizen who was born outside Ireland, you are entitled to become an Irish citizen, even if your parent derived Irish citizenship through marriage, adoption or naturalization and he/she was an Irish citizen at the time of your birth. If one of your grandparents is an Irish citizen who was born in Ireland, you may also become an Irish citizen, the Irish government said. If you were born on the island of Ireland — which includes the British province of Northern Ireland — before Jan. 1, 2005, you are entitled to be an Irish citizen.

Earlier this week, Flanagan said Ireland will do its utmost to protect the open borders between the British province of Northern Ireland and the Republic of Ireland after the 1998 Good Friday Agreement, which ended three decades of sectarian violence between Protestants and Catholics in Northern Ireland known as The Troubles. One of the challenges of Brexit, Flanagan said will be for Ireland to persuade the EU “of the need for specific arrangements which protect the key gains of the peace process on this island.”

The sudden popularity of Irish passports in the U.K. likely has little to do with its slower pace of life, green hills or friendly reputation — rather, It’s a gateway to the rest of Europe. As Kevin Warnes, a teacher in Shipley, West Yorkshire, told the Guardian newspaper last month: “I have two children and I want them to retain their EU citizenship. I want them to be able to travel, live and work freely in a Europe of open borders, to explore their near world with as much liberty as possible.”

British workers who fear losing their jobs with a Brexit could do worse than move to Ireland or anywhere else in the EU with an Irish passport in their back pocket. The EU sets a minimum paid vacation of 20 days per year, the standard in Ireland. But France mandates 30 days, followed by the U.K. (28 days) and Denmark, Finland, Norway and Sweden (25 days). (The U.S. is one of the few developed countries that does not require employers to provide paid time off.)

Big multinationals were drawn to Ireland over the last 20 years by low corporate tax and a well-educated, English-speaking work force. However, the construction boom and frenzy for housing was fueled by reckless lending of billions of euros by banks to property developers, resulting in a housing-market crash from which the country is still recovering. Ireland’s unemployment rate hovers at 7.8%, but that’s down from 9.8% just a year ago.

While economists debate whether London-based financial firms will move thousands of jobs overseas, the future of Ireland’s still-fragile economy is also uncertain. The U.K. is Ireland’s biggest trading partner, accounting for 12.4% of Irish goods exports and 20% of service exports, according to Standard & Poor’s. The U.K.’s exit from the EU would have a negative effect on the Irish economy “at least in the short to medium term,” the ratings agency said.