Next to nothing is known about the life of Henry Sherwin. He is mentioned by some scholars, for instance in the Sudelbücher of G. C. Lichtenberg, and his Tables were not only in public libraries but also in private possession of scholars like Gauss. But his person is not touched. Encyclopedia Britannica, British National Library, the voluminous work of Moritz Cantor, and even Wikipedia have no biographical data.
There are only few letters, for instance that one sent to Abraham Sharp of March 1704 which in full text is reproduced in
William Cudworth: Life and Correspondence of Abraham Sharp London (1889) and a letter from Edmond Halley of February 1704, belonging to the Macclesfiled Collection
The first edition of Sherwin's ordinary seven-figure tables of logarithms of numbers and trigonometrical functions appeared in 1705-6. It was reprinted in 1710, 1717, 1726, 1742, 1761, and 1771. In 1785 Hutton's new edition of Sherwin's Tables took the leading position and maintained it for a century. An overwiew about the editions and libraries holding Sherwin's Tables is given here. The Tables have been reprinted most recently by Ulan Press and by Forgotten Books.
From the preface of the 1726 edition we can obtain, that Henry Sherwin was alive at that time. The third edition in 1742 was edited by William Gardiner, so Sherwin was certainly no longer alive. The fourth and fifth edition, 1761 and 1771 respectively, were edited by Samuel Clark.
OCLC gives the following bibilographical data: born before 1690, died after 1717 and Janus gives born before 1700, died 1740
From the letter to Sharp we can obtain that, at the beginning of the 18th century, Henry Sherwin lived in London.