'Sherwin, Henry (fl. 1705-17), mathematician, editor of Mathematical tables (London, [1705]-1710): in 1705 he was planning a trip to Jamaica (letter to Sharp, RGO 1/69C, f.111r,v). Taylor (II). p.143; Cudworth, pp.171-74.'
I have ordered a copy of this letter'letter to Sharp' (RGO was the Royal Greenwich Observatory) and will report back with a transcript, also ordered the letter from Halley to Sherwin in the Macclesfield Collection mentioned in earlier Answer 1 as bothhaven't to date found a transcript of the latter in the public domain (both at same source (Cambridge, Cambridge Univ. Lib.)
Entry notes that the court records are at the Guildhall Library, London but not consulted by the Eds for firm letter date. I'm a long way from London to access. If the records include the debate that prompted Sherwin's query or of any other records of his activities there, it perhaps provides a lead on his background?