The name Melhado seems to be Portuguese in origin, but I have not absolutely confirmed this. Melhorar means 'to improve', so Melhorado means improved! It can be found in Jewish synagogue records in London, Amsterdam and Jamaica. It is one of the 'distinctive family names of the Sephardic Jews who comprised the majority of the Resettlement in England and the Jewish communities of Barbados, Jamaica and Nevis' according to "Jews, Slaves and the Slave Trade" (see below). The book goes on to say that 'virtually no Spanish or Portuguese individuals settled in England or the colonies [so] there is little risk in stating that bearers of such surnames ... were Jewish'. (For a general history of the Jews in Portugal, see THE SEPHARDIC JEWS IN PORTUGAL. For information about the Jews of Jamaica, see Jews of Jamaica.)
I do not not know much about this connection with Jamaica, but have discovered that there was quite a prominent Melhado family there. There's even an old print of Mrs. Melhado's garden in Montego Bay dating from the 1830s. This is probably the garden of Luna Melhado, the relict of Dr. Emanuel Melhado, who was buried in Montego Bay - parish of St. James - in 1853. In 1923, a Reggie Melhado purchased a large mansion in Kingston, Devon House, and this is documented in a book "Devon House Families" by Enid Shields (ISBN 976-8100-02-8). I have have found Jamaican Family Search useful for finding references to Jamaican ancestry: these seem particularly relevant to my family, though there are around 40 files (November 2001) with references to the Melhado family:
Daniel Melhado was a merchant with property in Kingston Jamaica and London. It seems from synagogue and tombstone records in Jamaica that he was initially based in Kingston, where most if not all his children were born, and then moved to London. He and his wife Judith died in London in 1838 and 1853 respectively: their deaths were registered and their burials noted in the records of the Novo Cemetery of the Spanish and Portuguese Jewish Congregation in London.
I found some additional information in Jews, Slaves, and the Slave Trade : Setting the Record Straight by Eli Faber (ISBN: 0814726380). It sets out to prove that Jewish involvement in the Slave trade was not very extensive and is packed with relevant statistics, with one-half of the book being bibliography, appendices and footnotes. There is lots of information for the researcher interested in Barbados, Jamaica and Nevis records. The author cites original sources such as shipping and tax records, stock-transfer ledgers, censuses, slave registers, and synagogue records.