This cameo is often considered among the group of so-called 'State Cameos', which includes the Gemma Augustea and other renowned pieces.
The Blacas Cameo (also known as the Strozzi Cameo) can be traced back to 1731, where it is described as being part of the collection of the Strozzi Cabinet in Florence. Sadly, its provenance earlier than this is unknown.
The figure originally wore a laurel-wreath, but this was replaced with a diadem decorated with smaller jewels and carved stones. 
An interesting feature of the Blacas Cameo is the Gorgon-emblazoned aegis that Augustus wears, as this was not a common feature of Augustan art or poetry, being associated with Minerva (Athena), while Augustus' principal cult association was with Apollo.
True, the Gorgoneion does feature in Augustan poetry, such as the description of it in Vulcan's forge (Virgil, Aeneid 8.435-438), but this is not explicitly linked with Augustus. Later emperors, notably Domitian, would make a far clearer association with Minerva and her aegis.
For more on gems in the BM, see:
Rudoe, Judy. “Eighteenth and Nineteenth-Century Engraved Gems in the British Museum; Collectors and Collections from Sir Hans Sloane to Anne Hull Grundy.” Zeitschrift Für Kunstgeschichte; 59, no. 2, 1996: 198–213.
jstor.org/stable/1482797
#AAOTD
Rudoe, Judy. “Eighteenth and Nineteenth-Century Engraved Gems in the British Museum; Collectors and Collections from Sir Hans Sloane to Anne Hull Grundy.” Zeitschrift Für Kunstgeschichte; 59, no. 2, 1996: 198–213.
jstor.org/stable/1482797
#AAOTD
