If Britian was defeated would Commonwealth countries fight on ?

If Britian was invaded by Germany in 1940 and forced to surrender unconditionally ( instead of a pre invasion peace deal ) What would happen to the Commonwealth countries like Canada, Australia ,New Zealand and South Africa? At that point in the war we were hardly much of a real threat to the Third Reich , but we were still at war with Germany and with America still neutral do we sue for peace or fight on as best we could and hope the U S A would soon join us ? what would our options be ?