One in Harley St botched cut (9)

I believe the answer is:

hairstyle

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'cut' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'one in harley st botched' is the wordplay.
'one' becomes 'i' (Roman numeral).
'in' indicates putting letters inside.
'botched' indicates an anagram.
'harley'+'st'='harleyst'
'harleyst' is an anagram of 'harstyle'.
'i' inserted within 'harstyle' is 'HAIRSTYLE'.

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(Other definitions for hairstyle that I've seen before include "Pageboy or bob, say" , "Design of crowning glory" , "DA possibly" .)

I've seen this clue in The Sun.

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