LONDONDERRY, Northern Ireland — Crossing the border between Northern Ireland and the Irish Republic used to involve delays, checkpoints, bureaucratic harassment and the lurking threat of violence. That it’s now virtually seamless — that you can drive across without even knowing it — feels close to miraculous.

It is also one of the great successes of the Irish peace process of the last several decades. “It was like you had to climb over a locked gate,” George Fleming, the president of the Londonderry Chamber of Commerce, said in an interview. “And then someone came and opened the gate.”

But as with so many British-related matters these days, “Brexit” — Britain’s divorce from the European Union — has thrown this hard-won arrangement into jeopardy.

If the British government succeeds in extricating itself from the European Union, the two parts of Ireland will lose one of their most important connective threads: a shared membership in the bloc. In an instant, one part of the island would be in Europe, and the other would not.