Story involving British item of furniture (5)
I believe the answer is:
table
'item of furniture' is the definition.
(table is a type of furniture item)
'story involving british' is the wordplay.
'story' becomes 'tale' (synonyms).
'involving' indicates putting letters inside.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'tale' enclosing 'b' is 'TABLE'.
(Other definitions for table that I've seen before include "Chart; present formally" , "Data arranged in rows and columns" , "Flat surface on legs" , "Statistical chart" , "put forward for consideration" .)