regarding Edward Barnard, the Agent for the Crown Colonies.
Edward was the son of Edward Barnard, Rector of Alverstoke, 30 Sep 1763 - 23 Oct 1840 and Mary Ann Beadon, c 1764 - 12 Oct 1850. They married 22 Jul 1784 St James Westminster. His father was indeed the Edward Barnard who died in 1781. He was 1754 Headmaster of Eton, 1760 Canon of Windsor, Chaplain to King George III, 1765 Provost of Eton.
http://www.archive.org/stream/memoirsofcelebra02jessiala/memoirsofcelebra02jessiala_djvu.txt Mary Ann Beadon was the daughter of Mary Ann Watson and Edwards Beadon, Rector of North Stoneham, Hampshire, and also Chaplain to King George III in 1760. Mary Ann Watson was the daughter of Sir William Watson the scientist. 1715 - 1787.
Lots of information on the Beadon and Barnard families, so let me know exactly what you are interested in.
Cheers, Duncan