Broughton was born at Westminster and educated well for his day, including at The King's School, Canterbury, where he was a King's scholar. His fortunes turned from commerce to theology when he inherited a substantial sum, allowing him to study at Cambridge University. He graduated as a Bachelor of Arts in 1818, and was also in that year ordained deacon and priest and married to Sarah Francis. He became a Master of Arts in 1823. He first became a curate in Hampshire, then later in Surrey where he became noticed by the Duke of Wellington who materially assisted his prospects, including certain influence in Broughton being offered the Archdeaconry of Sydney.
Broughton arrived in Sydney on 13 September 1829, succeeding Thomas Scott as Archdeacon of New South Wales (that at the time substantially encompassed what is now the states of New South Wales plus Queensland to the north and Victoria to the south.) At this time, the colony was ecclesiastically an Archdeaconry of the Diocese of the Bishop of Calcutta.
Broughton was promptly made a member of both the colony's legislative council and executive council, assisting the Governor in the administration. He was granted a leave of absence and returned to England in 1834, there championing the cause of the church. The result was not as he expected; the diocese of Australia was to be formed. He was enthroned Bishop of Australia on 5 June 1836, just days after his arrival from England.
Broughton travelled to England in late 1852 and was involved in administration and missionary fund raising. Broughton died in London in February 1853, and is buried in Canterbury Cathedral.
Broughton made many journeys around the fledgling colony and is credited as instigating the building of many churches in places such as Newcastle and the Hunter Valley north of Sydney and in the Monaro region inland to the south-west.
Broughton championed the Newcastle case, and forfeited 500 pounds Sterling from his salary to partly fund the development of a new diocese.
St. Andrew's Cathedral, Sydney, was commenced during the late 1840s.
Bishop Broughton also consecrated Saint Mary on Allyn, Allynbrooke, in the Hunter Valley. His son-in-law, William Barker Boydell, married his daughter Mary Phoebe, and the Bishop ordered that a church be built for his daughter to worship in. William Boydell and Mary Phoebe are both buried at Saint Mary on Allyn, along with their son, Henry, who died when he was one year old.