Their bliss is shattered in the United Kingdom (7,5)

I believe the answer is:

british isles

I'm a little stuck... Click here to teach me more about this clue!

'the united kingdom' is the definition.
The definition and answer can be both locations as well as being singular nouns.
Maybe there's an association between them I don't understand?

'their bliss is shattered' is the wordplay.
'shattered' indicates anagramming the letters.
'their'+'bliss'+'is'='theirblissis'
'theirblissis' anagrammed gives 'BRITISH ISLES'.

'in' acts as a link.

Can you help me to learn more?

(Another definition for british isles that I've seen is " UK and Ireland".)

I've seen this clue in The Globe and Mail.

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