Like millions of other British citizens, Paul Gadsdon from Somerset was unhappy with the result of the EU referendum. He values the feeling that he is European, and the freedom to live and work across most of the continent. But unlike many others, he had a get-out-of-jail-free card: an Irish-born grandfather, which meant he could apply for citizenship there and obtain an EU passport.

So Gadsdon set about pulling together the sequence of birth and marriage certificates that would be the first step in becoming a fully-fledged Irishman.

It’s a two-step process: first, the applicant has to prove Irish heritage and obtain citizenship via the Foreign Births Register.

Then they have to separately apply for an Irish passport. And it’s not cheap – anyone applying is likely to have to spend nearly £500 on fees and certificates, but with Britain heading to a crash-out Brexit, Gadsdon thought it was worth it.

But two years after he began the process, he is disillusioned. Ireland’s Department of Foreign Affairs has cashed his cheques – but done almost nothing in return.

As he says: “I spent a year gathering evidence (birth, marriage, death certificates), along with certified copies of identification, to get dual Irish citizenship through its foreign birth registry, and I haven’t heard a thing since. That was one year ago, and I was told it would take six months.

“I know they have been swamped, but I did pay €278. It’s not so much the application, or the money – it’s all the documentation that I needed to apply, that I need back. It took around a year to get the 20 or so legal documents in order to start this application.”

What irks Gadsdon and some other applicants, is that the Irish authorities cash the payment immediately on receipt of an application, knowing that it won’t be examined for months if not longer.

Even when Gadsdon obtains his citizenship, he is likely to face another nine-month wait or longer – plus the €80 fee – to obtain a passport.

Tim Minogue, from Lewes, Sussex, shares Gadsdon’s concerns. “I submitted the online form and paid the fee in late September last year, followed up by the notarised copies of my UK passport and the various family birth/death/marriage certificates required.

“I received an emailed acknowledgement of receipt of the completed application in October. Since then, not a dickybird.”

Minogue says emails to the Irish authorities have not produced replies, while phone calls go unanswered.

Meanwhile, the information on the Irish government’s website seems to vary, he says, with some saying that applications will take six months, and others six to nine months. Eleven months on, he’s still waiting. “Of course you have got to be sympathetic as they are obviously dealing with a flood of applications,” says Minogue, who is contemplating retirement in Ireland.

“It’s just that nothing happens … on the DFA site there is a phone number, but it either just rings and rings, or it takes you to a recorded message. I sent a polite email but did not receive a reply.”

He says he feels in limbo, not knowing if his application has gone astray, if he has sent the correct documentation, or if he will have to re-apply.

“I have no way of finding out. And there will then be another long delay when I can actually apply for a passport,” he says.

The Irish authorities told Guardian Money that it has, indeed, been deluged with applications from Britain, but has now created a new team to deal with the rush.

The DFA says: “Until 2016 the number of applications for Foreign Births Registration was relatively low, at approximately 6,000 a year. The department has seen an increase in the number of applications, from approximately 6,000 in 2015 to over 25,000 in 2018. More than 19,000 applications have been received already in 2019. The majority in 2019 have come from Great Britain (over 11,000 to date).”

It added that even a straightforward application for citizenship can take six to nine months to process, and that complex ones can take up to 12 months.