In part, it's a London beauty parlour (5)
I believe the answer is:
salon
'beauty parlour' is the definition.
(synonyms)
'in part it's a london' is the wordplay.
'in part' indicates the answer is hidden within the clue.
'SALON' is hidden within 'its a london'.
(Other definitions for salon that I've seen before include "Reception room - social gathering" , "Call loudly" , "Loans out as a reception room" , "Literary gathering" , "Beauty parlour" .)