Almost defeated accepting British weakness (6)
I believe the answer is:
foible
'weakness' is the definition.
(a foible is a weakness or failing)
'almost defeated accepting british' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'defeated' becomes 'foiled' (foil can mean to defeat or thwart).
'accepting' indicates putting letters inside.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'foiled' with its final letter taken off is 'foile'.
'foile' going around 'b' is 'FOIBLE'.
(Other definitions for foible that I've seen before include "Harmless peculiarity in person's character" , "Minor eccentricity" , "Harmless peculiarity or mannerism" , "Quirk" , "weakness" .)