Ships from northern European ports didn't produce passenger lists on arrival in the UK unless their voyage had started further away. So I've been lucky to find someone who joined a ship in Italy - because the ship's voyage started in India and thence through Suez. Unless therefore the ship was for example sailing from Bremen or Hamburg via Southampton to New York, you'll be out of luck.
I have no idea at all whether the German authorities kept lists - or if they did, whether the lists survive.