Thanks for the links. I had looked at jamaicanfamilysearch before: they have detailed lists of the immigrants 1840-41 when a new system was introduced, but nothing for the period before, which what I need.
The second link was intriguing, and a great find, but those logs are only for the Royal Navy warships, i.e. not passenger ships.
I guess I'm trying to find who might have kept such passenger lists (Customs? Agent General of Immigration?) or whether they are centrally stored at e.g. Kew, or in each port city. A possibility is CO384 or CO386 at Kew. The records after 1890 are computerized and available online at findmypast.co.uk, but I need the earlier period.