Bragge was born in Birmingham in 1823. He studied mechanics, mathematics and engineering and at the age of 22, began an illustrious career in railway design. His career saw him travel all over the world, but in particular South America, Egypt, Russia and Europe. Bragge was an inveterate collector, and he acquired material from wherever he travelled. During the 1850s, Bragge helped create railways in Brazil and Argentina. Whilst here, he acquired many important fossils of South American megafauna such as the armadillo-like Glyptodon and giant ground sloth Megatherium. His collection ultimately became very eclectic and included books by Cervantes from Spain, ancient Egyptian artefacts and metalwork from around the world. In particular, he was fascinated with tobacco and tools associated with smoking and collected these wherever he travelled. His association with Sheffield began in 1858, when he took up the directorship of John Brown and Company.
Throughout the 1860s, Bragge involved himself with Sheffield politics becoming a Searcher in the Cutlers Company in 1864 and rising through the ranks to become the Master Cutler in 1870. Part of his motivation for seeking office seems to have been in establishing a museum of craft and design, specialising in metalwork in Sheffield. Having failed to convince fellow cutlers of this need during his tenure as Master, Bragge sought a position on the town council. In 1871, he was returned as the council member for Ecclesall, and placed on the council's Free Libraries Committee, which Bragge would barely ever attend. Significantly, in 1873 Bragge donated much of his prized collection to Birmingham Free Library. That same year, Sheffield council agreed to establish a free public museum at Weston Park. As a result, the Sheffield's Free Libraries Committee also became responsible for the establishment of the museum, and Bragge became far more engaged. As such, he was an influential figure in the founding of Weston Park Museum, but his vehement insistence of focussing entirely on craft, design and metalwork resulted with him falling out with many influential individuals, not least John Ruskin, Henry Clifton Sorby and the museum's first Curator, Charles Callaway, who was effectively bullied out of the position by Bragge after just 10 months. Bragge would eventually sell some of his collection to Sheffield in 1877.
Today, Bragge is an interesting and controversial figure, and an example of the kinds of individuals who are ripe for deconstruction from the point of view of decolonisation. On the one hand, most of his travels were a result of his expertise. He was generally invited to the countries he visited in order to work on capital infrastructure projects. Unusually for a British Victorian, the countries he visited were often not the usual haunts of the British Empire. On the other hand, how he acquired the material he collected is not known and is most likely unknowable. It is also clear that he considered museums to be tools of Global Capitalism and of Empire, established to give British manufacturers a competitive edge in markets around the world.