Insect giving British man illness (6)
I believe the answer is:
bedbug
'insect' is the definition.
(bedbug is a kind of insect)
'giving british man illness' is the wordplay.
'giving' says to put letters next to each other.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'man' becomes 'ed' (short for Edward).
'illness' becomes 'bug'.
'b' put next to 'ed' is 'bed'.
'bed'+'bug'='BEDBUG'
(Other definitions for bedbug that I've seen before include "It feeds on blood at night" , "Night-time biter" , "It sucks your blood while you sleep" , "Night-time bloodsucker" , "Little sucker" .)