It seems the confusion has been clarified!
The difference between the two William Bartons Stock Brokers…
Robert Dodge Barton’s son William (1805-1852) = Maria Jackson 7 Jul 1823 St Matthew, Bethnal Green. He was a Stock Broker of 1 Trafalgar Place West, Shoreditch in 1851. PROBATE : Will of William Barton, Stock Broker of No 1Trafalgar Place, West Hackney Road, Middlesex 28 Jul 1852. One of his sons was Thomas Jackson Jackson Barton born 8 Nov 1826, baptised 24 Dec 1826 St Leonard Shoreditch
WHEREAS…
Sir Edmund Barton’s father was
William GILES Barton (1795 – 1881), the youngest son of a London Perfumer (Edward Barton). He married Mary Louise Whydah 26 May 1827 St George Hanover Square, Westminster. William was the accountant of the Australian Agricultural Company, and later, for many years, the only, sharebroker in Sydney.
http://thepeerage.com/p47365.htmhttps://uoncc.wordpress.com/2007/12/17/archives-of-the-australian-agricultural-company-uon/