I found more information about William Shawn & William Priest in the book " The Marks of the London Silversmiths and Goldsmiths", c. 1697-1837, by John P. Fallon
William Priest was the son of William Priest and was apprenticed to Richard Gurney on 30 July 1740.He obtained his freedom on 6 september 1749, and was made a Liveryman in March 1758 and died between 1802 and 1811.
William Shawn II was the son of Thomas Shawn (Dry Cooper) and was apprenticed to John Swift on 11 November 1736.He obtained his freedom on 6 April 1748 and was made a Liveryman in April 1751.
In the Parliamentary Return of 1773, he is recorded as a plate worker of Bishopsgate Street.
Hope this helps!