Since you say US to UK then was he in the U.S. Merchant Service? This is a very comprehensive website on how and where to do research. He may not have had a "service number" as the Military had them. It was only in the 1980s they received WWII Military Service Credit. He may be listed on passengers/crew lists of the time before and after, if not during the war. the name "marines" and "Navy" do not necessarily the US Marines or US Navy, there where US Army Armed Guards put on ships for protection.
http://www.usmm.org