Many thanks for your replies. I don't think they really answer my question as what I should have mentioned is that my family had already left Germany as they were fleeing the Nazis so I don't think they would have risked going back.
It's a shame the answer doesnt lie with the Swedish American line. If they stopped operating in 1939 then I'm running out of ideas.
I do know that there were flights between Sweden and the UK during the early parts of the war (orange painted JU 52s) but am assured ordinary civilians would not have been allowed to travel.
Thanks again.