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Wedge was born in Cambridgeshire, England; he was the eldest son of Edward Davy Wedge and a nephew of John Helder Wedge. In 1824, he emigrated to the Colony of Van Diemens Land (later Tasmania) with his father, uncle and cousin, John Charles Darke.
Charles Wedge worked initially as an assistant government surveyor with the Survey Department in Van Diemen's Land.
He resigned in 1836, to work with John Helder Wedge on a sheep station in the Port Phillip District (later the Colony of Victoria). Charles Wedge managed the family's property at Werribee and then established a sheep station in the Western District of Victoria.
"these depredations did not cease till many lives were sacrificed, and, I may say, many thousands of sheep destroyed". 
In the mid-1860s, he became a shareholder in the Denison Plains Pastoral Company (often referred to as the Denison Plains Association), which was founded with the intention of settling in North-West Australia on the Denison Plains (a remote area in what would be known later as the south-east Kimberley).
Following the failure of the Denison Plains scheme, Wedge was employed at Roebourne as a Western Australian government surveyor. Among other projects, in 1866 the Government Resident, Robert John Sholl tasked Wedge with finding a suitable harbour in the Port Hedland area, to enourage and service settlement further north, in areas such as the De Grey River. The natural harbour of Port Hedland itself was already considered unsuitable, due to the thick mangroves. Following heavy, unseasonal rain and swollen tidal creeks, Wedge was unable to reach the harbour itself or find another site. Wedge reported: "Independently of the Port being difficult of access from the land sides, the want of a natural supply of water must always be a serious impediment to its being made available as a shipping port." He also felt that the deep sand and lack of wood for building made the area unsuitable.
- Public Library, Museums; Bride, Thomas Francis (1898). Letters from Victorian pioneers, being a series of papers on the early occupation of the colony, the aborigines, etc. University of California Libraries. Melbourne : R. S. Brain.
- "Denison Plains Association". The Inquirer & Commercial News. 10 May 1865. p. 2. Retrieved 19 Dec 2013.
- "Nicol Bay". The Inquirer & Commercial News. 3 August 1866. p. 3. Retrieved 19 Dec 2013.
- Wedge, Charles (8 August 1866). "Exploration". The Inquirer and Commercial News. Perth, WA. p. 2. Retrieved 2 May 2017.