Hello David
Your Peter Eul, from near Bruhl, lived right on the Rhine. So it is reasonable to assume that they would have traveled down the Rhine to Antwerp and departed for England from there. River travel was still much cheaper than rail in 1862.
My Peter Eull, from the Eifel, did just that trip to get to the sea to catch a sailing barque ("May Flower", in fact) in Antwerp for New York in 1846.
I have not been able to establish any connection between Euls and Eulls but they must be related in some way. I would be delighted to hear about it if anyone has made such a connection.
Good hunting
Bill Eull, Canada