DUNDALK, Ireland — Gerard McEvoy’s daily commute across the border between his home in the United Kingdom and his workplace in Ireland takes just 10 minutes, and the only hint that he is in a different country is when the road signs change from miles to kilometers.

But that all-but-invisible border between Northern Ireland and Ireland may end up a victim of Britain’s decision in June to leave the European Union. With Ireland still a member of the bloc, a new arrangement for the flow of people and goods will have to be negotiated. And the border is just one challenge in what is likely to be a much broader redefinition of the relationship between Britain and Ireland, another example of the sprawling and often unintended consequences of Britain’s choice to split from Europe.

Partly as a result of their shared membership in the European Union, London and Dublin have largely put aside historical animosities and developed a tightly woven relationship. Now Britain’s exit from the bloc holds the risk of introducing new friction, from the economy to the management of Northern Ireland’s sectarian tensions to the familial, social and cultural ties that bind the inhabitants of the islands.

“The border has been out of sight, out of mind — there’s been no trouble,” Mr. McEvoy said, standing in his department store in Dundalk and recalling how he grew up during the Troubles.