The little creature had run inside for asylum (8)

I believe the answer is:

madhouse

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'for asylum' is the definition.
(madhouse is a kind of asylum)

'the little creature had run inside' is the wordplay.
'the little creature' becomes 'mouse' (mouse is a kind of creature. I am not sure about the 'little' bit.).
'run' indicates an anagram.
'inside' indicates putting letters inside.
'had' with letters rearranged gives 'adh'.
'mouse' going around 'adh' is 'MADHOUSE'.

Can you help me to learn more?

(Other definitions for madhouse that I've seen before include "asylum" , "state of chaos" , "badly run establishment?" , "9d 21d [BEDLAM]" , "State of uproar and total confusion" .)

I've seen this clue in the Evening Standard.

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