UK Ports Passenger Lists 1878-1960
AncestorsOnBoard, part of FindMyPast.com has UK outbound passenger lists 1890 – 1960
Ancestry.co.uk has UK incoming passenger lists 1878 – 1960 which contain the names of people arriving at United Kingdom ports from places outside Europe.
This National Archives leaflet gives more details.
Both the above sites are free to search, but require payment to view the records. They are free to view at the National Archives. Some Libraries may have free access, refer Miscellaneous tips. Some Genealogy Societies provide free access if you are a member.