Sir Charles Asgill, 1st Baronet (17 March 1713 – 15 September 1788), merchant banker, was the third son of Henry Asgill, silkman, of St Clement Danes, Middlesex
Alderman of Candlewick Ward (1749–1771) Asgill was also Master of the Worshipful Company of Skinners (1749), a Governor of Bridewell (1743–1750), Sheriff of the City of London (1753) and Lord Mayor of London (1757–1758).
Article in Wikipedia [1]: that for his son and namesake, the 2nd Baronet can be found here [2].
The James Boswell web page is [3]