Cars cross the controless border between Ireland and Northern Ireland, in Donegal | Paul Faith/AFP via Getty Images Brits flood Ireland with passport applications after Brexit vote Post office runs out of applications as Irish foreign affairs minister warns extra demand risks ‘clogging up the system.’

The number of U.K. citizens applying for Irish passports has surged as Brits rush to secure EU citizenship after the country voted to leave the bloc in last week's referendum, AFP reports.

"There has been an increase in queries in respect of entitlements to Irish passports in recent days," a spokeswoman for the Irish embassy in London said.

A post office in Belfast, Northern Ireland, had to erect signs warning it had run out of applications. "Due to the increased demand for Irish passport forms we have currently run out. We have an emergency order to meet the extra demand coming on Tuesday,” signs stated.

People whose parents were born in Ireland are entitled to a passport. Figures from 2011 suggest there are around 430,000 Irish-born people in Britain, with one in four people in the U.K. having Irish heritage.

Irish Foreign Affairs Minister Charlie Flanagan on Monday warned the extra applications risked clogging up the system at its busiest time and causing further delays, the Irish Times reports.

Other EU countries have reported similar trends. Dozens of Britons have applied to become Belgian citizens, according to broadcaster VRT, while Swedish Radio reports that a record number of Brits have applied for Swedish citizenship over the weekend. Over 100 Brits filed their application in just three days, compared to 440 applications for the whole of 2015.

Meanwhile, Bulgarian Prime Minister Boyko Borisov said on Saturday that Britons based in the country were "welcome" to apply for citizenship.