Pop off right away from Bloomsbury thoroughfare (2,4)
I believe the answer is:
go west
'pop off' is the definition.
(thesaurus)
'right away from bloomsbury thoroughfare' is the wordplay.
'right' becomes 'r' (common abbreviation).
'away from' suggests deleting specific letters.
'bloomsbury thoroughfare' becomes 'gowerst' (Gower Street).
'gowerst' with 'r' taken away is 'GO WEST'.
(Other definitions for go west that I've seen before include "travel advice to youngster" , "- -, Young man, said during US expansion" , "Fail" , "comedy film" , "Return from Japan, perhaps" .)