The Galtons were well-known in Bristol and Birmingham, and had made a tidy fortune in iron mongering, gun manufacturing and banking. Ultimately the name can be traced back to the village of Galton in the county Dorset. Galtons had also practiced law in Bristol in the 17th century. John Galton (1671-1743) had joined the Quakers in the early 1700s, on his marriage into the Quaker Button family, and the Galtons were Quakers until Francis' father Samuel Tertius Galton (1783-1844) converted to the Church of England in 1807. John Galton had married into the Quaker Button family, his son Samuel (1720-99) married into the Quaker Farmer family, and his grandson Samuel John (1753-1832, Francis' grandfather) married into the Quaker Barclays (now famous for their banking connections). So paternally Francis was related to the Quaker stock in many lines, an inheritance which was reinforced by the Quaker tendency to intermarry: his grandmother Lucy Barclay was a Barclay by at least three lines.
Samuel married Lucy BARCLAY, daughter of Robert BARCLAY and Lucy BARCLAY, in 1777. (Lucy BARCLAY was born in 1757 and died in 1817.)