Applications for Irish passports from people based in Britain are up by 70 per cent this year
Dan Mulhall added applications for Irish citizenship through grandparents had also increased "quite dramatically" amidst a surge in applications after Brexit.
People born in Northern Ireland have an automatic right to Irish citizenship, while British people with an Irish parent, or in certain circumstances an Irish grandparent, also have an automatic right to become Irish citizens.
"We've seen significant percentage increases, the overall numbers are still not dramatic," Ambassador Mulhall told Radio 4's Today programme.
"The increase this year, the first few months of this year, over last year is up 70 per cent, that's the demand for Irish passports from people based in Britain.
Ambassador Mulhall said that Brexit complicates the idea of a united Ireland
While around 50,000 Irish passports were usually issued in Britain each year, 70,000 were issued in 2016, Ambassador Mulhall said.
Brexit complicates the situation for everyone in Ireland
The ambassador, who is due to leave his post to become the Irish ambassador to the US, also told Today a border poll on a united Ireland could be "something that will arise at some time in the future".
"Brexit complicates the situation for everyone in Ireland," he said.
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Brexit debate in pictures Mon, April 17, 2017
The debate in the European Parliament in Strasbourg will focus on key issues of the Brexit talks including reciprocal rights for EU citizens, the peace process in Northern Ireland and trade
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Former leader of the UK Independence Party (UKIP) Nigel Farage (L) gestures as he speaks with EU Commission president Jean-Claude Juncker (R) prior to a debate on the conclusions of the last European Council, at the European Parliament in Strasbourg
70,000 Irish passports were issued in Britain in 2016
"We would prefer if Britain were to remain in the European Union, that would be the most straightforward way of maintaining the good situation we have with Northern Ireland."
Ambassador Mulhall also said talks over the border in Ireland were "in a good position" given the recognition on all sides to maintain a soft border after Brexit.