As a result I object to leaving home in London (4)
I believe the answer is:
soho
'in london' is the definition.
'as a result i object to leaving home' is the wordplay.
'as a result' becomes 'so'.
'i object' becomes 'me'.
'to leaving' is a deletion indicator.
'home' with 'me' taken away is 'ho'.
'so'+'ho'='SOHO'
(Other definitions for soho that I've seen before include "London's nightlife centre" , "Colourful London show-biz district" , "Exotic London district popular with tourists" , "(Formerly) disreputable area of London" , "Entertainment district in London's West End" .)