After their mother's death, Barton moved south and married Elizabeth Horne (1760–1833) of Tottenham, Middlesex, by whom he had a son, John Barton, an economist who specialized in the study of poverty.
Following their mother’s demise, Barton moved to the south and married Elizabeth Horne (1760–1833), from Tottenham, Middlesex, with whom he had a son named John Barton, an economist specializing in poverty studies.