Daniel Mulhall said many of a record 500,000 applications in the first half of 2017 had come from British people who fear losing their rights to live and work in the EU after withdrawal.
That increase comes on the back of a 40 per cent rise in the number of Britons seeking Irish passports in the second half of 2016, immediately after the EU referendum.
“It’s risen very significantly,” Mr Mulhall told BBC Radio 4’s Today programme. “We have to attribute that to the impact of last year’s referendum.”
On the 500,000 applications from around the world, the outgoing ambassador said: “That’s an extraordinary number of passports - well up on our previous numbers.
“People around the world, many of them maybe British people living in Europe, living elsewhere with Irish connections, are looking for Irish passports to safeguard their positions for the future.”
The figures were revealed ahead of the Irish Taoiseach warning Brexit will affect “every single aspect of life in Northern Ireland”, in his first speech north of the border.
Leo Varadkar will also meet Northern Ireland's political parties, after talks to restore power sharing at Stormont broke down in acrimony.
“The challenge in our generation is Brexit,” Mr Varadkar will say, in a speech at Queen’s University in Belfast.
“The Brexit negotiations are well under way in Brussels. And, to quote Michel Barnier [the EU’s Brexit negotiator], the clock is ticking.
“Every single aspect of life in Northern Ireland could be affected by the outcome, jobs and the economy, the border, citizens' rights, cross border workers, travel, trade, agriculture, energy, fisheries, aviation, EU funding, tourism, public services, the list goes on.”
In October, the Irish premier will, as part of the EU Council, discuss whether sufficient progress has been made in the Brexit negotiations for them to move onto future trade.
“The three key issues are citizens' rights, the financial settlement and issues relating to Ireland,” Mr Varadkar will say.
“It is my fervent hope that progress will have been made, but I do not underestimate the challenges we face.”
Earlier this week, Mr Varadkar said he was working to “keep the door open” for Britain to halt Brexit, amid growing rows over the future border with the North.
Mr Varadkar is pushing for the Irish Sea to become the post-Brexit border with the UK, warning Ms May that her plan to use smart technology was doomed and would jeopardise the peace process.
In the interview, Mr Mulhall rejected suggestions that amounted to a “land grab”, but said the Republic wanted the UK to remain in the EU customs union.
“I think people are now beginning to realise the complexities of leaving the European Union, and there's a debate developing here.” he said.
“Remaining in the customs union would resolve many of these issues on the border of the isle of Ireland - that seems to us to be a practical solution.”
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