You can search and download lists of ships’ passengers entering and leaving the United Kingdom from and for ports outside Europe and the Mediterranean.
These are digitised records from two record series held at The National Archives:
passengers who arrived in the UK between 1878 and 1960 (BT 26) at Ancestry.co.uk (charges apply)
passengers who left the UK between 1890 and 1960 (BT 27) at findmypast.co.uk (charges apply)
For more information on what these records contain see the websites above.
Please note that BT 27 is also available on Ancestry.co.uk (charges apply).