There are also extensive records of interest to the Jamiacan researcher available (on subscription) on Jamaican Family Search. Jacob & Rebecca's marriage is listed in a list of Jewish marriages and there are also lists of Jewish births and many other useful references.
These appear to show the following children: those shown with an asterisk * are mentioned in Judith's will (see below).
His business is listed in London directories. It's not shown in the 1828 or 1829 Pigott directories. In various 1830 & 1831 London directories (e.g. Robson), Daniel Melhado is shown as a merchant at 8 East India Chambers - the building street address seems to have been 23 Leadenhall Street. In 1830, there's also a David Dias there. In 1836, the company is at 2 Adams Court, Old Broad Street and there's also a Melhado & Silva listed there. In Pigot 1839, the firm is shown as Melhado & Co, merchants. In the Post Office directory of 1841 (available on the historical directories web site), Daniel is still listed at 71 Guilford Street but the company name is shown as Melhado, John A & Co, 2 Adams ct, Old Broad st. By 1844, the company is Melhado & Magnus, merchants, at the same address. By 1847, it seems that Moses Magnus, merchant, had dropped the Melhado name and moved to 20 Gt. Prescot Street, Goodman's Fields.
I have not yet discovered exactly what the company traded, but there is a much later clue. In the 1901 census, there is a Abraham Arthur MELHADO staying at Smedley's Hydro in Matlock. He is described as a Jamaican Merchant Trader (Coffee, Pimento, Sugar &c) - so it's very likely that this person is related.
Daniel died in 1838 aged 60: on the certificate his death was reported by a "nephew" whose name looks like Jo A Melhado (presumably from the 1841 directory entry also his business partner) but who appears also to be his son-in-law Jacob Aaron Melhado who was later executor of (Daniel's wife) Judith's will. The "D. Melhado & nephew" who contributed $32 to the relief of the 1831 Barbados hurricane (see Subscribers to the Barbados Hurricane Relief Fund) must also be Daniel & Jacob/John.
It seems that Daniel & Judith attended the Bevis Marks synagogue in London. The records of the Novo Cemetery of the Spanish and Portuguese Jewish Congregation show a burial of Daniel Hens Melhado on 28 Jan 1838 and his will was proved the next month. He left everything to his wife Judith. Judith was buried next to him on 13 Feb 1853 aged 63. Her will is rather more informative and throws some light on the rest of the family.
Notable points from Judith's will which was written in 1851:
The Bevis Marks marriage records show the marriage of Sarah to Alfred - this indicates that Alfred was the son of Emanuel (and hence of Luna, Judith's 'sister'). With all these Melhado girls marrying other Melhados, it seems that there were lots of marriages of cousins!
The cemetery records also show another Elias Melhado and his widow Leah buried on 10 Mar 1884 and 30 May 1892 respectively. There are several other Melhados buried here, notably Sarah Henriques Melhado (dau. of Daniel) on 22 Dec 1816. "Bella of Elias" Melhado buried on 4 Dec 1851 may also be related.
The birth records do not appear to have connections.