William Dawson, clock and watchmaker, London, England.  Died there in 1820.

Page 77 of Watchmakers and Clockmakers of the World lists William Dawson as a freeman of the Clockmakers Company from 1778, a liveryman from 1801 and deceased in 1820.
The Will of William Dawson, late watch case maker of King’s Head Court, Gutter Lane, was granted probate on 28th January 1820 (National Archives reference PROB11/1624/417).

Surviving examples of his work are dated to 1778 and to 1801. [Watchmakers & Clockmakers of the World.  G.H. Baillie.  1947, London]

This watch is dated to 1780.