LONDON — When Britain leaves the European Union at the end of the month, it must secure trade ties to the Continent, revamp its migration rules and reset relations with global partners like the United States, to name just a few looming challenges.

But the question gripping Brexit supporters is whether the moment of departure will be marked by the familiar chimes of Big Ben.

Inconveniently, the country’s most famous clock tower is under repair, like much of the crumbling parliamentary estate, yet that has not stopped a vigorous campaign to bring it back to life for a brief moment of history.

“Big Ben Must Bong For Brexit,” screamed a front-page headline in the British tabloid The Daily Express, which was superimposed on a picture of the clock minus the scaffolding and cladding that conceal it.