Depends on how you define important.
Tiger Moth -probably one of the best training aircraft until Cessna and Piper starting building aircraft in large numbers post war.
Auster-sold all over the commonwealth. Saw service in the military and also sent to the Artic and Antarctic with various expeditions.
Bristol Freighter-not going to win a beauty contest but designed to do a job.
Argosy -likewise designed for a purpose and in some ways revolutionised the freight industry with quick turnaround capability.
DH Dove- short haul airliner, used in Australia for aeromedical, charter, freight etc.
DH Heron- used by airlines, military etc.
HS748/Andover-used by the both the military as well as civilian airlines across the globe.
Britten Norman Islander-landrover with wings, probably easier to name a country that has not operated it.
Vickers Viscount
DH Comet
DH Rapide
DH 86
On the military front
Spitfire
Hurricane
Lancaster
Vulcan
Lightning
Harrier.