A British exit, known as Brexit, would most likely stoke renewed pressure in Scotland for independence from Britain — an idea rejected in a 2014 referendum but one that has not gone away.

A vote to leave the bloc would also put Northern Ireland on the external frontier of the European Union. And it would present challenges to the formal and informal integration of North and South that has accelerated in the wake of the complex 1998 peace agreement that defused the long sectarian conflict between pro-British Protestants and pro-Irish Catholics in the North.

In doing so, it could risk reversing a process during which, in the words of Mary McAleese, a former Irish president, customs and border controls have “melted away.” While Northern Ireland is unlikely to opt for new constitutional arrangements with the British government in London and the Irish government in Dublin anytime soon, were it to feel “the cold winds of a serious economic downturn” after a British divorce from Europe, there might be a “new political dynamic” there, she added.

Even a vote to remain could have constitutional implications if Scottish and Northern Irish votes swung a close result in favor of staying, antagonizing English supporters of leaving.