On the verge of critical attack ousting the British (8)
I believe the answer is:
roadside
'on the verge' is the definition.
(side or verge of the road)
'critical attack ousting the british' is the wordplay.
'critical attack' becomes 'broadside' (I've seen this in another clue).
'ousting' indicates named letters should be taken away.
'the british' becomes 'b' (abbreviation e.g. in 'BBC').
'broadside' with 'b' removed is 'ROADSIDE'.
'of' acts as a link.
(Other definitions for roadside that I've seen before include "kerb" , "Area adjoining carriageway" , "Bordering on the street" , "Oddly enough, the edge of the thoroughfare is adored" , "Carriageway border" .)