Weapon that's annoyed London area (8)
I believe the answer is:
crossbow
'weapon' is the definition.
(I know that crossbow is a type of bow)
'annoyed london area' is the wordplay.
'annoyed' becomes 'cross' (cross can mean angry).
'london area' becomes 'bow' (I've seen this in other clues).
'cross'+'bow'='CROSSBOW'
'that's' is the link.
(Other definitions for crossbow that I've seen before include "Old weapon with mechanism for firing arrow" , "historic weapon" , "Weapon firing bolts" , "can precipitate a quarrel" , "One responsible for shooting bolts" .)