Last weekend, shortly before he sat down to watch Ireland play England in the rugby Six Nations championship, Kevin Warnes posted the application form to renew his Irish passport. Though Warnes was born and has always lived in England and considers himself “completely English”, his mother is originally from Ireland, which allowed him to obtain dual citizenship as a young man in the 1980s when he was doing a lot of travelling in Europe.

A teacher from Shipley in West Yorkshire, he had allowed his Irish passport to lapse. But the prospect of Britain potentially voting to leave the EU in June “propelled me into action”, he says.

“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.” As soon as he gets his own passport back, Warnes will apply for Irish citizenship for his teenage daughters as well. “I certainly wouldn’t have done that if it wasn’t for Brexit.”

Figures obtained by the Guardian suggest he is far from alone. According to Ireland’s Department of Foreign Affairs, the number of British-born people applying for Irish passports on the basis of their ancestry has risen sharply in the past year, just as the debate over the UK’s potential withdrawal from the EU has intensified before June’s referendum.

Between 2014 and 2015, the number of adults born in England, Scotland or Wales applying for their first Irish passport on the basis of having an Irish-born grandparent increased by more than 33%, from 379 to 507. Applications from those with one or more Irish parent rose by 11% in the same period, from 3,376 to 3,736. In the previous year, the total applying in both categories fell slightly.

Ireland offers automatic citizenship to anyone with an Irish parent, regardless of where they were born, while the grandchildren of citizens are also entitled to claim a passport once their births have been recorded in the country’s foreign births register. Great-grandchildren may also be eligible if their parents had registered by the time of their birth. It has been estimated that as many as six million Britons can claim an Irish-born grandparent.

Northern Ireland is a special case, with anyone born north of the border having the same rights to claim Irish citizenship as elsewhere in the island. There, too, first-time adult applications for Irish passports rose by 14% from 10,672 to 12,159 between 2014 and 2015. Both Britain and Ireland allow citizens to hold dual citizenship.

An Irish government spokeswoman said applicants were not asked their reasons for applying for a passport and so the rise could not be attributed to a single cause.

But anecdotal evidence suggests that the risk of a British leave vote has been a decisive factor for many. Ireland is one of the most pro-European countries in the EU and would be highly unlikely to vote to leave, despite harsh austerity conditions imposed by Brussels as part of a multibillion-euro bailout in 2010.

Siobhan Mooney from London has never even been to Ireland but told the Guardian she decided to apply for citizenship through her Irish-born grandfather because she was getting “quite panicky” at the prospect of a British withdrawal. “I thought, well, if I get my Irish passport then at least if the UK is kicked out I’ve got some legal protection if I want to go and enjoy free movement in Europe.” She said she knew at least two other people who were considering doing the same thing.

Glen O’Hara, a professor of modern and contemporary history at Oxford Brookes University, said he hadn’t absolutely decided to claim citizenship through his Northern Irish-born grandfather “but it’s nice to know that there’s a fallback position in case Britons really do prove willing to give up their rights as European Union citizens”.

He said he was less concerned with the practicalities of free moment after a potential Brexit – “I should think we’ll join the EEA [European Economic Area] and there’ll be few if any more border controls anyway” – but with the principle of “maintaining my European-ness”.

“I am a European Union citizen as things stand, I regard myself as a European and I don’t see why anyone else has the right to drag me out of that. So I’m thinking of taking a relatively painless joint citizenship route to ensure that I can keep my EU identity and rights, whatever other UK citizens decide.”