City tent, rude about cleaner establishment (10)

I believe the answer is:

laundrette

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'cleaner establishment' is the definition.
The definition suggests a singular noun which matches the answer.

'city tent rude about' is the wordplay.
'city' becomes 'LA' (Los Angeles).
'about' is an anagram indicator.
'tent'+'rude'='tentrude'
'tentrude' anagrammed gives 'undrette'.
'la'+'undrette'='LAUNDRETTE'

Can you help me to learn more?

(Other definitions for laundrette that I've seen before include "Washing establishment" , "On film, mine was beautiful" , "cleaning outfit" , "Wash-room" .)

I've seen this clue in The Daily Express.

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