It's not a flattering term for Great Britain but due to its catchy alliteration it has not run out of steam among newspaper editors.
Broken Britain is a term which has been used in The Sun newspaper, and by the Conservative Party to describe a perceived widespread state of social decay in the United Kingdom. The Sun has run frequent stories under the "Broken Britain" theme since 2007
In a parliamentary briefing entitled The problems of British society (2010) we learn
“Broken society” may be a catchy phrase, and useful for encompassing a variety of social ills, but what does it mean? (...) Tony Blair in 1995 asked us to look at “the wreckage of our broken society” and, using the now-familiar language of rights and responsibilities, called for a new civic society where everyone played a part. The phrase then really came into its own in the Conservative leadership campaign in 2005, first from Liam Fox and then with David Cameron taking up the term in his leadership acceptance speech.
In March 2010, political commentator and Lib-Dem, Adam Bell, talked about epithets and soundbites
It’s clear that the coming election will be fought over adjectives. Specifically, the adjectives one likes to place in front of ‘Britain’. Anyone with even a cursory interest in politics can’t help but notice the proliferation of phrases like ‘Blackout Britain’, ‘Breakdown Britain’ and other pejorative epithets riding on the back of Cameron’s ‘Broken Britain’ soundbite. (...) Unlike other soundbites, the ‘Britain’ line directly refers to contemporary society, so rather than being an easy way to encapsulate a policy pledge (i.e. ‘Education, education, education’), it becomes a method by which a politician can establish a shared identity with the electorate.
The writer Vron Ware argues in his book on the history of Britain's 21st century Commonwealth soldiers that Broken Britain is metaphorical
The term "Broken Britain" had become a clichè, operating as an expressive metaphor of a dysfunctional national community.
And in a paper published by the University of Edinburgh, by Tom Slater (2013). We have the following observation
The Myth of “Broken Britain”: Welfare Reform and the Production of Ignorance
(...) Cameron’s declamatory argument is clear and unequivocal: “big government” has “broken” Britain, and encouraged everyone to be “irresponsible”. “Broken Britain” in fact became the catchphrase of the 2010 general election, which many attributed to the Rupert Murdoch-owned tabloids. Whilst there is no question that Tory-boosting tabloids (and broadsheets) did indeed devote considerable ink to this moral panic, its origins lie in the activities and publications of Duncan-Smith’s CSJ.
So what is "Broken Britain"? Linguistically speaking, is it a metaphor, catch phrase, epithet, or a soundbite? I suggested it was a derogatory nickname for Great Britain in a previous answer of mine. Was I mistaken? Is it a metonymy because it represents the breakdown of British society and welfare? Why is it so linguistically powerful ?
I'd also appreciate knowing if the expression existed prior to 2005, it seems unlikely that nobody thought of it during the economic crisis of the 1970s before Margaret Thatcher came to power.