According to the ADB, Piddington was "brought up in the booktrade", and early in life worked at a bookshop in Bond Street, London. He was also possibly the William R. Piddington, described as a bookbinder,whose shop at 1 Birchin Lane, Cornhill was listed in a London Directory for 1839. If so, the information was slightly out of date - Piddington emigrated to New South Wales in 1838.
After a spell as a pastoralist in the Hunter Valley region, Piddington returned to Sydney and went into partnership with William Colman, an established Sydney bookseller, forming the firm of Colman and Piddington. As Colman left the colony shortly after the partnership began, an arrangement had presumably been made for Piddington to superintend the business in Colman's absence. In the event, Colman died at sea shortly after his departure from the colony, and Piddington narrowly avoided bankruptcy in discharging the firm's debts. Piddington then began a bookselling and publishing enterprise under his own name.
Piddington active in colonial politics. He was a member of the Anti-Transportation League, and after a brief period with the Sydney City Council, he began a long career as an MP in the New South Wales Legislative Assembly. He was active in the directorship of public institutions such as the Australian Subscription Library, and the Bank of New South Wales. On his death he left a large estate.