Jacob in Godwin's 1796 list for 1773, in the 1794 version Jacob is preceded by Jos (crossed out). In some of Godwin's autobiographical notes (these ones don't seem to be scanned online, I read them on microfilm Duke MF 75 in Bodleian Library) he wrote "Jacob's - admiration of Jos" shortly after his arrival in London 1773
John Jacob died 15.7.1804 in his 70th year. In his will (Nat Arch PROB11/1411) he made his brother Joseph of Fulham, coachmaker, an executor. In Ann Godwin's letter of 1805 (Abinger c.9 f2) she said of Mr Benford (who had just died) "he was a trustee for a 150 3 per cent stock for me had been ill ever since Mr Jacob died....wrote to Jo Jacob about it". Joseph Jacob was a coachmaker at various London addresses from 1767( 31 St Mary Axe to 1783, Greek St Soho from 1784), in his will proved 1832 he was called gentleman of Kensington (Nat Arch PROB11/1800). The uncoded Jacob entries in the diary were probably mostly Joseph, certainly after John Jacob died. The first entry, of 5.11.1791, Godwin called on Jacob and talked of Mrs John J; then on 8.11.1791 he called 'on Mrs Jacob, fr'. On 24.11.1791, after two more calls on Jacob (11.11.1791 and 22.11.1791) he supped at Jacob's and apologised 'to Mme'. The clearest reading would be that 5th Nov he called on Joseph Jacob, on 8th Nov on Mrs John Jacob and on 24th Nov supped at John Jacob's, but it is certainly ambiguous. (Another question is what 'fr' meant - see fr). 20.12.1791, 12.1.1792, 29.1.1792, 30.1.1792, 21.2.1792, 6.3.1792, 12.3.1792, 19.3.1792 and 16.4.1792 were mostly calls on Jacob and could have been either brother. On 4.1.1795 Jacobs dined at Tooke's, this is more likely another person (or possibly a plural), but 9.8.1796 when Jacob dined at J Johnson's it could have been one of the brothers. The call of 8.4.1801 was probably on Joseph as Soley who was there was probably Thomas Apreece Soley whose will PCC 1802 mentioned Joseph Jacob of Greek St Soho as a friend, and 10.4.1804 could have been either brother. After John Jacob's death, the entries were calls (mostly by Godwin) or meetings, and surely refer to Joseph (especially the two that mention Brompton where he lived): 31.5.1805, 24.7.1805, 25.7.1805, 31.7.1805, 17.8.1805, 16.10.1805, 23.10.1805, 25.11.1805, 27.11.1805, 20.7.1806, 26.10.1806, 25.4.1807, 28.4.1807, 19.10.1807, 28.10.1807, 15.6.1808, 17.6.1808, 22.8.1808, 12.12.1809, 13.12.1809, 30.12.1809, and 2.1.1810 (and a call on W Jacob of 29.3.1810). The contacts with Jacob didn't continue much after Ann Godwin's death until 1828 when they resumed. See also Abinger c.1 f32-3 and c.42 f14.
John Jacob's dau Sarah married Joseph Lancaster 23.6.1801 St Andr Holborn (not Joseph Lancaster DNB 1778-1838 educationist)