A little street nearby (5)

I believe the answer is:

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This clue could be a double definition.

'a little street' is the first definition.
'close' can be an answer for 'street' (thesaurus). I am unsure of the 'a little' bit.

'nearby' is the second definition.
(similar in meaning)

Can you help me to learn more?

(Other definitions for close that I've seen before include "Stop proceedings" , "on very affectionate terms" , "Near, mean or humid" , "residential street" , "Airless" .)

I've seen this clue in the Evening Standard.

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