Have you looked at Passenger Lists, leaving the UK?
Ancestry have them, as do FindMyPast.
You can probably fine Ancestry (freee usage) in your local library.
FindMyPast is free to look at the indexes, but you will need to buy credits to look at the actual lists.
For example, on the SS Caledonian, departing Glasgow 4th September 1909 for New York, are:
Joseph Stewart, 21, Fitter
William Stewart, 25, Joiner
Charles E Stewart, 30, Shipwright