I have confidently traced one line of the family to Elizabeth Watson who married John White, shoemaker, in 1802 at St George's church in Doncaster. The marriage was witnessed by Thomas Swift. Both bride and groom were of the parish.
Elizabeth was buried 8 February 1846 at St George, her age was 73 which makes her year of birth around 1773.
I found a baptism for Elizabeth:
8 March 1774, Elizabeth daughter of Thomas Watson
There are mother's details and no father's occupation but there are several other baptisms for children born to Thomas Watson (all St George, Doncaster):
Thomas, 2 Sep 1770
Thomas, 13 May 1772
William, 23 Apr 1776
Sally, 9 Feb 1777
Francis, 7 Jan 1778
Ann, 5 Apr 1778, father an innkeeper
Edwin, 26 Aug 1781, father an innkeeper, buried 15 Sep 1782
Henry, 13 Apr 1786, son of Thos and Ann, father an innkeeper
Sarah, 25 May 1787, dau of Thos and Ann, father an innkeeper
A Thomas Watson married Ann Sutcliff on 13 September 1769 at St George and up until now I've assumed these were the correct details. Then I noticed that there were 2 baptisms for children of Thomas Watson in 1778 - Francis and Ann - and were probably not twins, so am I looking at two different men??