Alien conquest in Barking of no significance (15)

I believe the answer is:

inconsequential

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'alien conquest in barking of no significance' is the definition.
I can't tell whether this defines the answer.

'alien conquest in barking' is the wordplay.
'barking' is an anagram indicator (UK slang for mad).
'alien'+'conquest'+'in'='alienconquestin'
'alienconquestin' is an anagram of 'INCONSEQUENTIAL'.

Can you help me to learn more?

(Other definitions for inconsequential that I've seen before include "Trivial" , "unrelated to the foregoing" , "Petty" .)

I've seen this clue in The Telegraph.

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