Automaton that's British in origin (5)
I believe the answer is:
robot
'automaton' is the definition.
('robot' can be a synonym of 'automaton')
'british in origin' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'in' means one lot of letters goes inside another.
'origin' becomes 'root' ('root' can be a synonym of 'origin').
'b' going into 'root' is 'ROBOT'.
'that's' is the link.
(Other definitions for robot that I've seen before include "programmed servant" , "Automated machine" , "Automation" , "Automaton or sci-fi creature" , "Soulless worker" .)