LONDON — When Billy Bragg’s “Take Down the Union Jack” climbed up the charts in 2002, the year Queen Elizabeth II was celebrating 50 years on the throne, few would have thought that it could become a legitimate call.

But less than two months before Scotland holds a referendum on whether to become independent, Mr. Bragg’s lyrics sound a little less preposterous:

Britain isn’t cool, you know

It’s really not that great

It’s not a proper country

It doesn’t even have a patron saint.

Certainly, if Scots vote to secede on Sept. 18, Great Britain will be less great and the United Kingdom no longer, well, united. So what might the kingdom-sans-Scotland be called? And could the Union Jack — a flag that combines the colors of the three patron saints of England, Scotland and Ireland — come down at last as demanded by Mr. Bragg, who is English but a staunch supporter of Scottish independence?

Anecdotally at least, there seems to be a desire for change: The Flag Institute, an educational group in Britain that offers guidance about flags and their usage, surveyed its members last November and found that nearly two in three respondents wanted a new flag if Scotland broke away. Nowhere does the issue resonate more than in Wales, which was annexed by England more than five centuries before the current flag was designed in 1801 and is the only nation not represented.