The stampede for Irish passports since the UK voted to leave the EU has been widely interpreted as an effort by Britons to avoid hassle at airports. Produce proof of an Irish granny and voilà, no matter what happens with Brexit, you have a burgundy passport and can travel freely throughout the EU.

For some, however, even those without Irish lineage, it signifies something more – they are moving to Ireland and plan to stay there. To really become Irish.

“I’m building up to be an Irish citizen, that’s the long-term goal,” said Keith Donaldson, 37, an office manager from Jarrow in north-east England who moved to Dublin last year.

Keith Donaldson plans to become a naturalised Irish citizen. Photograph: Keith Donaldson

In the 2016 referendum, he campaigned for the UK to remain in the EU. The result shocked him. When his employer, the law firm Lewis Silkin, opened a Dublin office, he seized the chance. “I grew up regarding myself European and wanted to maintain that,” Donaldson said.

He has no Irish lineage but can apply for naturalisation after five years’ residency. “Some things you can’t do unless you’re a citizen,” Donaldson said. “I’ve started getting involved in various political groups. It’s about contributing, being a member of Irish society. I identify myself as being a Brexit refugee.”

Other so-called Brexiles have experienced a similar phenomenon of relocating to Ireland in the aftermath of the Brexit vote and gradually embracing the idea that it will be long term, perhaps permanent.

Alexandre de Menezes on campus in Galway. Photograph: National University of Ireland Galway

“Moving here gave me the possibility to be here long enough and apply for citizenship. I have to be here for five out of nine years,” said Alexandre de Menezes, 39, a dual British-Brazilian national who teaches soil microbiology at National University of Ireland Galway. “Being half British was always important to my identity, but Brexit took some of the shine away.”

Kate Ryan, 40, a food writer from Bristol, married an Irish man and lived in Clonakilty, County Cork, for more than a decade without thinking much about nationality. Then came the referendum.

“It was always in the back of my mind that I would go for citizenship, but Brexit has forced my hand,” she said. This week, Ryan lodged an application for naturalisation. In the absence of Irish lineage, it entailed reams of paperwork and will cost about €1,500 (£1,285). “I decided to crack on and get this thing done.”

Kate Ryan, with a mic, at a food festival in Ireland. Photograph: Kate Ryan

Brexit should not affect the common travel agreement between Ireland and the UK, but the uncertainty makes anything possible, said Ryan. “Everything is so up in the air. This is very much about protecting my status,” she added.

Ryan is proud of her British heritage and regularly visits her parents – who voted for Brexit – in Wales. But she feels European. Becoming Irish would underline that identity: “I see it as an opportunity to redefine who I am and my place in the world.”

Mike Clarke, who recently left Brighton to take up a post as director of campus infrastructure at Trinity College Dublin, envisages putting down roots. “I plan to stay in Ireland as long as I can. UK plc will take an awful long time to heal,” he said.

Clarke, who grew up in Croydon, south London, has an Irish grandparent, so has a smooth path to citizenship. “I’m a very proud Englishman and British citizen. But I think of myself as European,” he said.

Applications for Irish passports have risen to record levels, with almost 250,000 requests since January, a 30% increase from the same period last year, according to the Department of Foreign Affairs and Trade. Of the 860,000 Irish passports issued last year, about 200,000 applications came from the UK.

For those with Irish lineage, the process of gathering paperwork and engaging with family history can trigger a genuine connection with Ireland, said Marc Scully, a psychology lecturer at Mary Immaculate College in Limerick with a special interest in migration and the Irish diaspora.

“It may start off pragmatically thinking ‘I’ll be in the right queue in the airport’, then becomes emotional, more of a psychological process of identification,” he said.

Kieran Fitzpatrick at NUI Galway. Photograph: National University of Ireland Galway

Kieran Fitzpatrick, 30, who grew up in England with Irish parents, now researches medical history at NUI Galway.

“Brexit could be awful for Ireland in terms of economic consequences, but from an emotional landscape, it’s been a nice feeling to be removed from it. It’s a very sad period in British history,” he said.

Bill Foster has made a new life in Dublin. Photograph: Bill Foster

Bill Foster, the managing director of the Irish division of the immigration consultancy Fragomen, said he probably would not stay long enough to obtain citizenship. But for now, he is glad to have swapped London for Dublin.

“There’s a feeling here that we want to move forward and not hanker back to the past. Living here has made me feel more European in many ways,” he said.

• This article was amended on 8 April 2019 to clarify a quotation.