Dr Knox 9.11.1791 at Bosse's / Knox 13.1.1802 at Wycombe's / 6.9.1821 Knox dies / 27.6.1828 call on Dr Knox
The 1791 and 1821 entries above have been coded on the GD website to Vicesimus Knox DNB 1752-1821, correctly in my view. The 1802 entry (which is uncoded in GD website) may have been him also but no special reason to think so. Of the Knox entries in the Dictionary of Irish Biography the one with the most radical sympathies was George Knox 1765-1827, the others were stong government supporters. The 1802 entry could well have been him. The Dr Knox of 1828 was certainly Thomas Knox 1784-1843 (in his father Vicesimus' DNB entry). He obtained DD in 1824 and was on holiday in Hastings when Godwin called on him (Bodleian Abinger c43 f29)

Work notes: 
William Knox DNB 1732-1810 government official and pamphleteer (of conservative tendency) / William Knox DNB 1762-1831 Church of Ireland bishop of Derry / Alexander Knox DNB 1757-1831 theological writer / 1800 Thomas Knox counsel 13 Soho Sq, William Knox (his father) Soho Sq & Lanstonia, Haverfordwest, Pembs / James Knox & Joseph Ward attornies 13 Newman St, Oxford St & 32 Duke St Piccadilly1800 / General (John d 1800 Dict Irish Biog) Knox 12 Grafton St, Mrs Knox 6 Grafton St Fitzroy Sq 1800 / G Knox Esq 4 Kings Bench Walk Temple 1800 (Dict Irish Biog 1765-1827) / Henry Knox esq 74 Baker St Portman Sq / plenty more in PCC wills and Alum Ox, Cantab, Dublin