The official lists of passengers leaving British ports and held at the PRO start in 1890 and are arranged year by year under the port of departure [BT 27]. Details include the occupation and age of each passenger and usually the place of residence in the UK. Passengers pre-1890 are usually recorded on arrival in Australia and New Zealand with varying amounts of personal details given. - And from what Lois Ralph wrote, they were similarly recorded on arrival in the USA.
There are many groups of shipping transcribers available via the Internet, with alphabetical indexes to ships and to passengers.
http://olivetreegenealogy.com/ships/search_ships.shtml gives a free 14 day search. There are many others as well, and most are free.